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{{Numeral systems}}
The '''duodecimal''' system (also known as '''[[Radix|base]]-12''' or '''dozenal''') is a [[positional notation]] [[numeral system]] using [[12 (number)|twelve]] as its [[radix|base]]. In this system, the number [[10 (number)|ten]] may be written as "A", "T" or "X", and the number [[11 (number)|eleven]] as "B" or "E" (another common notation, introduced by Sir [[Isaac Pitman]], is to use a rotated "2" (ᘔ) for ten and a reversed "3" (Ɛ) for eleven). The number twelve (that is, the number written as "12" in the [[decimal|base ten]] numerical system) is instead written as "10" in duodecimal (meaning "1 [[dozen]] and 0 units", instead of "1 ten and 0 units"), whereas the digit string "12" means "1 dozen and 2 units" (i.e. the same number that in decimal is written as "14"). Similarly, in duodecimal "100" means "1 [[gross (unit)|gross]]", "1000" means "1 [[great gross]]", and "0.1" means "1 twelfth" (instead of their decimal meanings "1 hundred", "1 thousand", and "1 tenth").


The number twelve, a [[highly composite number]], is the smallest number with four non-trivial [[integer factorization|factors]] (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the [[subitizing]] range. As a result of this increased factorability of the [[radix]] and its divisibility by a wide range of the most elemental numbers (whereas ten has only two non-trivial factors: 2 and 5, with neither 3 nor 4), duodecimal representations fit more easily than decimal ones into many common patterns, as evidenced by the higher regularity observable in the duodecimal multiplication table. As a result, duodecimal has been described as the optimal number system.<ref>{{cite web
{{Expert-subject|Physics|talk=Attention_from_an_expert_nomination|reason=uninformative from an encyclopedic standpoint|date=December 2013}}
| url=http://io9.com/5977095/why-we-should-switch-to-a-base+12-counting-system
| title=Why We Should Switch To A Base-12 Counting System
| author=George Dvorsky
| date=2013-01-18
| accessdate=2013-12-21 }}
</ref> Of its factors, 2 and 3 are [[prime number|prime]], which means the [[multiplicative inverse|reciprocals]] of all [[smooth number|3-smooth]] numbers (such as 2, 3, 4, 6, 8, 9...) have a [[terminating decimal|terminating]] representation in duodecimal. In particular, the five most elementary fractions ({{frac|1|2}}, {{frac|1|3}}, {{frac|2|3}}, {{frac|1|4}} and {{frac|3|4}}) all have a short terminating representation in duodecimal (0.6, 0.4, 0.8, 0.3 and 0.9, respectively), and twelve is the smallest radix with this feature (because it is the [[least common multiple]] of 3 and 4). This all makes it a more convenient number system for computing fractions than most other number systems in common use, such as the [[decimal]], [[vigesimal]], [[binary numeral system|binary]], [[octal]] and [[hexadecimal]] systems, although the [[sexagesimal]] system (where the reciprocals of all [[regular number|5-smooth]] numbers terminate) does better in this respect (but at the cost of an unwieldy multiplication table and a much larger number of symbols to memorize).


== Origin ==
{{Beyond the Standard Model|expanded=Supersymmetry}}
:''In this section, numerals are based on decimal [[Numerical digit|places]]. For example, 10 means [[10 (number)|ten]], 12 means [[12 (number)|twelve]].''
In [[particle physics]], '''supersymmetry''' ('''SUSY''') is a proposed extension of [[Spacetime symmetries|spacetime symmetry]] that relates two basic classes of elementary particles: [[boson]]s, which have an integer-valued [[Spin (physics)|spin]], and [[fermion]]s, which have a half-integer spin.<ref name = DarkMatter>Sean Carroll, Ph.D., Cal Tech, 2007, The Teaching Company, ''Dark Matter, Dark Energy: The Dark Side of the Universe'', Guidebook Part 2 page 60, Accessed Oct. 7, 2013, "...Supersymmetry -- A hypothetical symmetry relating bosons to fermions..."</ref> Each particle from one group is associated with a particle from the other, called its [[superpartner]], whose spin differs by a half-integer. In a theory with [[broken symmetry|unbroken]] supersymmetry each pair of superpartners shares the same mass and internal quantum numbers besides spin, but since no superpartners have been observed yet, supersymmetry must be a [[spontaneously broken symmetry]]{{citation needed|date=February 2013}}. The failure of the [[Large Hadron Collider]] to find evidence for supersymmetry has led some physicists to suggest that the theory should be abandoned.<ref>{{cite journal |last=Wolchover |first=Natalie |title=Supersymmetry Fails Test, Forcing Physics to Seek New Ideas |magazine=Scientific American |date=November 29, 2012 |url=http://www.scientificamerican.com/article.cfm?id=supersymmetry-fails-test-forcing-physics-seek-new-idea}}</ref> Experiments with the Large Hadron Collider also yielded an extremely rare [[particle decay]] event which casts doubt on supersymmetry.<ref>http://www.bbc.co.uk/news/science-environment-23431797 [[BBC]]</ref> A major weakness of SUSY is that it is not falsifiable, because its breaking mechanism and the minimum mass above which it is restored are unknown. This minimum mass can be pushed upwards to arbitrarily large values, without disproving the symmetry.


Languages using duodecimal number systems are uncommon. Languages in the [[Nigeria]]n Middle Belt such as [[Janji language|Janji]], [[Gbiri-Niragu language|Gbiri-Niragu]] (Gure-Kahugu), [[Piti language|Piti]], and the Nimbia dialect of [[Gwandara language|Gwandara]];<ref>{{Cite conference
Supersymmetry differs notably from currently known symmetries in that it establishes a symmetry between classical and quantum physics, which up to now has not been observed in any other domain. While any number of bosons can occupy the same [[quantum state]], for fermions this is not possible because of the [[exclusion principle]], which allows only one fermion in a given state. But when the occupation numbers become large, quantum physics approaches the [[classical limit]]. This means that while bosons also exist in classical physics, fermions do not. That makes it difficult to expect that bosons, if at all, possess the same [[quantum number]]s as fermions.<ref>[[Richard M. Weiner]], [[Spin-statistics-quantum number connection]] and supersymmetry, Phys. Rev. D 87 (2013) 055003-05,  arXiv:1302.0969</ref>
| title=Decimal vs. Duodecimal: An interaction between two systems of numeration
There is only indirect evidence for the existence of supersymmetry, primarily in the form of evidence for [[Minimal Supersymmetric Standard Model#Gauge Coupling Unification|gauge coupling unification]].<ref name="GKane">[[Gordon L. Kane]], ''The Dawn of Physics Beyond the Standard Model'', [[Scientific American]], June 2003, page 60 and ''The frontiers of physics'', special edition, Vol 15, #3, page 8 "Indirect evidence for supersymmetry comes from the extrapolation of interactions to high energies."</ref> However this refers only to [[electroweak]] and [[strong interactions]] and does not provide the ultimate unification of all interactions, since it leaves gravitation untouched.
| last=Matsushita
| first=Shuji
Supersymmetry is also motivated by solutions to several theoretical problems, for generally providing many desirable mathematical properties, and for ensuring sensible behavior at high energies. Supersymmetric [[quantum field theory]] is often much easier to analyze, as many more problems become exactly solvable. When supersymmetry is imposed as a ''local'' symmetry, Einstein's theory of [[general relativity]] is included automatically, and the result is said to be a theory of [[supergravity]]. It is also a feature of a candidate of a [[theory of everything]], [[superstring theory]].
| conference=2nd Meeting of the AFLANG, October 1998, Tokyo
| year=1998
| url=http://www3.aa.tufs.ac.jp/~P_aflang/TEXTS/oct98/decimal.html
| archiveurl=http://web.archive.org/web/20081005230737/http://www3.aa.tufs.ac.jp/~P_aflang/TEXTS/oct98/decimal.html
| archivedate=2008-10-05
| accessdate=2011-05-29
| postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}
}}</ref> the [[Chepang language]] of [[Nepal]]<ref>{{Cite book
| contribution=Les principes de construction du nombre dans les langues tibéto-birmanes
| first=Martine
| last=Mazaudon
| title=La Pluralité
| editor-first=Jacques
| editor-last=François
| year=2002
| pages=91–119
| publisher=Peeters
| place=Leuven
| isbn=90-429-1295-2
| url=http://halshs.archives-ouvertes.fr/docs/00/16/68/91/PDF/numerationTB_SLP.pdf
| postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}
}}</ref> and the [[Maldivian language|Mahl language]] of [[Minicoy Island]] in [[India]] are known to use duodecimal numerals. In fiction, [[J. R. R. Tolkien]]'s [[Elvish languages]] use a hybrid decimal–duodecimal system, primarily decimal but with special names for multiples of six.<!--this really depends on what version of the languages you are talking about. the later versions are as described here, but some earlier versions are truly pure duodecimal.-->


[[Germanic languages]] have special words for 11 and 12, such as ''eleven'' and ''twelve'' in [[English language|English]], which are often misinterpreted as vestiges of a duodecimal system.{{citation needed|date=January 2012}}  However, they are considered to come from [[Proto-Germanic]] *''ainlif'' and *''twalif'' (respectively ''one left'' and ''two left''), both of which were decimal.<ref>{{cite book|last=von Mengden| first=Ferdinand| year=2006|chapter=The peculiarities of the Old English numeral system|title=Medieval English and its Heritage: Structure Meaning and Mechanisms of Change|editors=Nikolaus Ritt, Herbert Schendl, Christiane Dalton-Puffer, Dieter Kastovsky|publisher=Peter Lang Pub|series=Studies in English Medieval Language and Literature |volume=16 |location=Frankfurt|pages= 125–45}}<br/>{{cite book|last=von Mengden |first=Ferdinand |year=2010| title=Cardinal Numerals: Old English from a Cross-Linguistic Perspective|series=Topics in English Linguistics| volume=67|location= Berlin; New York|publisher=De Gruyter Mouton| pages=159–161}}</ref>
A central motivation for supersymmetry close to the [[Electronvolt|TeV]] energy scale is the resolution of the [[hierarchy problem]] of the [[Standard Model]]. Without the extra supersymmetric particles, the [[Higgs boson]] mass is subject to quantum corrections which are so large as to naturally drive it close to the [[Planck mass]] barring its [[fine tuning]] to an extraordinarily tiny value. In the [[Minimal Supersymmetric Standard Model|supersymmetric theory]], on the other hand, these quantum corrections are canceled by those from the corresponding superpartners above the supersymmetry breaking scale, which becomes the new characteristic [[naturalness (physics)|natural]] scale for the Higgs mass. Other attractive features of TeV-scale supersymmetry are the fact that it often provides a candidate [[dark matter]] particle at a mass scale consistent with thermal relic abundance calculations,<ref>Jonathan Feng: [http://theory.fnal.gov/jetp/talks/feng.pdf Supersymmetric Dark Matter ''(pdf)''], University of California, Irvine, 11 May 2007</ref><ref>Torsten Bringmann: [http://www.desy.de/~troms/teaching/SoSe11/DM_slides_05.pdf The WIMP "Miracle" ''(pdf)''] University of Hamburg</ref> provides a natural mechanism for [[electroweak symmetry breaking]] and allows for the precise high-energy [[Grand unification theory|unification]] of the [[weak interactions|weak]], the [[strong interactions|strong]] and [[electromagnetism|electromagnetic]] interactions. Therefore, scenarios where supersymmetric partners appear with masses not much greater than 1 TeV are considered the most well-motivated by theorists.<ref>http://profmattstrassler.com/articles-and-posts/lhcposts/what-do-current-mid-august-2011-lhc-results-imply-about-supersymmetry/</ref> These scenarios would imply that experimental traces of the superpartners should begin to emerge in high-energy collisions at the [[LHC]] relatively soon. As of September 2011, no meaningful signs of the superpartners have been observed,<ref name="ATLAS SUSY search documents">[https://twiki.cern.ch/twiki/bin/view/AtlasPublic/SupersymmetryPublicResults#Early_2011_Data_5_CONF_Notes ATLAS SUSY search documents]</ref><ref name="CMS SUSY search documents">[https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsSUS CMS SUSY search documents]</ref> which is beginning to significantly constrain the most popular incarnations of supersymmetry. However, the total parameter space of consistent supersymmetric extensions of the Standard Model is extremely diverse and can not be definitively ruled out at the LHC.


Historically, [[Unit of measurement|units]] of [[time]] in many [[civilization]]s are duodecimal. There are twelve signs of the [[zodiac]], twelve months in a year, and the [[Babylonians]] had twelve hours in a day (although at some point this was changed to 24). Traditional [[Chinese calendar]]s, clocks, and compasses are based on the twelve [[Earthly Branches]]. There are 12 inches in an imperial foot, 12 ounces in a [[troy weight|troy]] pound, 12 [[British One Penny coin (pre-decimal)|old British pence]] in a [[shilling]], 24 (12×2) hours in a day, and many other items counted by the [[dozen]], [[gross (unit)|gross]] ([[144 (number)|144]], [[square number|square]] of 12) or [[great gross]] ([[1728 (number)|1728]], [[cube (arithmetic)|cube]] of 12). The Romans used a fraction system based on 12, including the [[uncia (length)|uncia]] which became both the English words ''[[ounce]]'' and ''inch''. Pre-[[Decimal Day|decimalisation]], [[Republic of Ireland|Ireland]] and the [[United Kingdom]] used a mixed duodecimal-vigesimal currency system (12 pence = 1 shilling, 20 shillings or 240 pence to the [[pound sterling]] or [[Irish pound]]), and [[Charlemagne]] established a monetary system that also had a mixed base of twelve and twenty, the remnants of which persist in many places.
Another theoretically appealing property of supersymmetry is that it offers the only "loophole" to the [[Coleman–Mandula theorem]], which prohibits spacetime and internal [[Symmetry (physics)|symmetries]] from being combined in any nontrivial way, for [[quantum field theory|quantum field theories]] like the Standard Model under very general assumptions. The [[Haag-Lopuszanski-Sohnius theorem]] demonstrates that supersymmetry is the only way spacetime and internal symmetries can be consistently combined.<ref>R. Haag, J. T. Lopuszanski and M. Sohnius, "[http://www.sciencedirect.com/science/article/B6TVC-4718W97-YF/1/bc160d55fb6a0faddac181fcff6871ce All Possible Generators Of Supersymmetries Of The S Matrix]", Nucl. Phys. B 88 (1975) 257</ref>


The importance of 12 has been attributed to the number of lunar cycles in a year, and also to the fact that humans have 12 finger bones ([[Phalanx bone|phalanges]]) on one hand (three on each of four fingers).<ref>{{Cite web
The [[Minimal Supersymmetric Standard Model]] is one of the best studied candidates for [[physics beyond the Standard Model]].
| title=ヒマラヤの満月と十二進法 (The Full Moon in the Himalayas and the Duodecimal System)
| last=Nishikawa
| first=Yoshiaki
| year=2002
| url=http://www.kankyok.co.jp/nue/nue11/nue11_01.html
| accessdate=2008-03-24
| postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}
}}{{dead link|date=January 2014}}</ref> It is possible to count to 12 with your thumb acting as a pointer, touching each finger bone in turn. A traditional [[finger counting]] system still in use in many regions of Asia works in this way, and could help to explain the occurrence of numeral systems based on 12 and 60 besides those based on 10, 20 and 5. In this system, the one (usually right) hand counts repeatedly to 12, displaying the number of iterations on the other (usually left), until five dozens, i. e. the 60, are full.<ref name=Ifrah>{{Cite book
  | last = Ifrah
  | first = Georges
  | author-link = Georges Ifrah
  | title = The Universal History of Numbers: From prehistory to the invention of the computer
  | publisher = [[John Wiley and Sons]]
  | year= 2000
  | page =
  | isbn = 0-471-39340-1
  | postscript = <!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}
}}. Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk.</ref><ref name=Macey>{{Cite book|last=Macey|first=Samuel L.|title=The Dynamics of Progress: Time, Method, and Measure|year=1989|publisher=University of Georgia Press|location=Atlanta, Georgia|isbn=978-0-8203-3796-8|page=92|url=http://books.google.com/books?id=xlzCWmXguwsC&pg=PA92&lpg=PA92|postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}}}</ref>


== Places ==
== History ==
In a duodecimal place system, [[10 (number)|ten]] can be written as ᘔ, [[11 (number)|eleven]] can be written as Ɛ, and twelve is written as 10. For alternative symbols, see [[#Advocacy and "dozenalism"|below]].
A supersymmetry relating [[mesons]] and [[baryons]] was first proposed, in the context of hadronic physics, by [[Hironari Miyazawa]] in 1966. This supersymmetry did not involve spacetime,  that is it concerned internal symmetry, and was badly broken. His work was largely ignored at the time.<ref>{{Cite journal
|author=H. Miyazawa
|year=1966
|title=Baryon Number Changing Currents
|journal=Prog. Theor. Phys.
|volume=36
|pages=1266–1276
|doi=10.1143/PTP.36.1266
|issue=6
|bibcode = 1966PThPh..36.1266M }}</ref><ref>{{Cite journal
|author=H. Miyazawa
|year=1968
|title=Spinor Currents and Symmetries of Baryons and Mesons
|journal=Phys. Rev.
|volume=170
|issue=5
|pages=1586–1590
|doi=10.1103/PhysRev.170.1586
|bibcode = 1968PhRv..170.1586M }}</ref><ref>[[Michio Kaku]], ''Quantum Field Theory'', ISBN 0-19-509158-2, pg 663.</ref><ref>[[Peter Freund]], ''Introduction to Supersymmetry'', ISBN 0-521-35675-X, pages 26-27, 138.</ref>


According to this notation, duodecimal 50 expresses the same quantity as decimal [[60 (number)|60]] (= five times twelve), duodecimal 60 is equivalent to decimal [[72 (number)|72]] (= six times twelve = half a gross), duodecimal 100 has the same value as decimal [[144 (number)|144]] (= twelve times twelve = one gross), etc.
J. L. Gervais and [[Bunji Sakita|B. Sakita]] (in 1971),<ref>{{cite doi|10.1016/0550-3213(71)90351-8|noedit}}</ref> [[Yuri Golfand|Yu. A. Golfand]] and [[Evgeny Likhtman|E. P. Likhtman]] (also in 1971), and D.V. Volkov and V.P. Akulov (in 1972),<ref>D.V. Volkov, V.P. Akulov, Pisma Zh.Eksp.Teor.Fiz. 16 (1972) 621; Phys.Lett. B46 (1973) 109; V.P. Akulov, D.V. Volkov, Teor.Mat.Fiz. 18 (1974) 39</ref> independently rediscovered supersymmetry in the context of quantum field theory, a radically new type of symmetry of spacetime and fundamental fields, which establishes a relationship between elementary particles of different quantum nature, bosons and fermions, and unifies spacetime and internal symmetries of the microscopic world. Supersymmetry with a consistent Lie-algebraic graded structure on which the Gervais−Sakita rediscovery was based directly first arose in 1971<ref>{{cite doi|10.1103/PhysRevD.3.2415|noedit}}</ref> in the context of an early version of [[string theory]] by [[Pierre Ramond]], [[John H. Schwarz]] and [[André Neveu]].


== Comparison to other numeral systems ==
Finally, [[Julius Wess|J. Wess]] and [[Bruno Zumino|B. Zumino]] (in 1974)<ref>{{cite doi|10.1016/0550-3213(74)90355-1|noedit}}</ref> identified the characteristic renormalization features of four dimensional supersymmetric field theories, which singled them out as remarkable QFTs, and they and [[Abdus Salam]] and their fellow researchers introduced early particle physics applications. The mathematical structure of supersymmetry ([[Graded Lie superalgebra]]s) has subsequently been applied successfully to other areas of physics, in a variety of fields, ranging from [[nuclear physics]],<ref>{{cite doi|10.1103/PhysRevLett.44.772|noedit}}</ref> [[critical phenomena]],<ref>{{cite doi|10.1103/PhysRevLett.52.1575|noedit}}</ref> [[quantum mechanics]] to [[statistical mechanics|statistical physics]]. It remains a vital part of many proposed theories of physics.
[[File:Dozenal multiplication table.png|thumb|right|300px|A dozenal multiplication table]]
The number 12 has six factors, which are [[1 (number)|1]], [[2 (number)|2]], [[3 (number)|3]], [[4 (number)|4]], [[6 (number)|6]], and [[12 (number)|12]], of which 2 and 3 are [[prime number|prime]]. The decimal system has only four factors, which are [[1 (number)|1]], [[2 (number)|2]], [[5 (number)|5]], and [[10 (number)|10]]; of which 2 and 5 are prime. Vigesimal adds two factors to those of ten, namely [[4 (number)|4]] and [[20 (number)|20]], but no additional prime factor. Although twenty has 6 factors, 2 of them prime, similarly to twelve, it is also a much larger base (i.e., the digit set and the multiplication table are much larger). Binary has only two factors, 1 and 2, the latter being prime. Hexadecimal has five factors, adding 4, [[8 (number)|8]] and [[16 (number)|16]] to those of 2, but no additional prime. Trigesimal is the smallest system that has three different prime factors (all of the three smallest primes: 2, 3 and 5) and it has eight factors in total (1, 2, 3, 5, 6, 10, 15, and 30). [[Sexagesimal]]—which the ancient [[Sumerians]] and [[Babylonia]]ns among others actually used—adds the four convenient factors 4, 12, 20, and 60 to this but no new prime factors. The smallest system that has four different prime factors is base 210 and the pattern follows the [[primorial]]s. In all base systems, there are similarities to the representation of multiples of numbers which are one less than the base.{{-}}<!-- the {{-}} template keeps the multiplication table from squeezing the heading for the next section-->


== Conversion tables to and from decimal ==
The first realistic supersymmetric version of the Standard Model was proposed in 1981 by [[Howard Georgi]] and [[Savas Dimopoulos]] and is called the [[Minimal Supersymmetric Standard Model]] or MSSM for short. It was proposed to solve the [[hierarchy problem]] and predicts superpartners with masses between 100 GeV and 1 TeV.
To convert numbers between bases, one can use the general conversion algorithm (see the relevant section under [[Base conversion|positional notation]]). Alternatively, one can use digit-conversion tables. The ones provided below can be used to convert any duodecimal number between 0.01 and ƐƐƐ,ƐƐƐ.ƐƐ to decimal, or any decimal number between 0.01 and 999,999.99 to duodecimal. To use them, the given number must first be decomposed into a sum of numbers with only one significant digit each. For example:


123,456.78 = 100,000 + 20,000 + 3,000 + 400 + 50 + 6 + 0.7 + 0.08
As of September 2011, no meaningful signs of the superpartners have been observed.<ref name="ATLAS SUSY search documents"/><ref name="CMS SUSY search documents"/> The [[Large Hadron Collider]] at [[CERN]] is producing the world's highest energy collisions and offers the best chance at discovering superparticles for the foreseeable future.


This decomposition works the same no matter what base the number is expressed in. Just isolate each non-zero digit, padding them with as many zeros as necessary to preserve their respective place values. If the digits in the given number include zeroes (for example, 102,304.05), these are, of course, left out in the digit decomposition (102,304.05 = 100,000 + 2,000 + 300 + 4 + 0.05). Then the digit conversion tables can be used to obtain the equivalent value in the target base for each digit. If the given number is in duodecimal and the target base is decimal, we get:
After the discovery of the [[Higgs particle]] in 2012, it was expected that supersymmetric particles would be found at CERN, but there has been still no evidence of them. The LHCb and CMS experiments at the LHC made the first definitive observation of a [[Strange B meson]] decaying into two muons, confirming a standard model prediction, but a blow for those hoping for signs of supersymmetry.<ref>[http://phys.org/news/2013-07-cern-latest-supersymmetry.html CERN latest data shows no sign of supersymmetry – yet] Phys.Org, 25 July 2013</ref> [[Neil Turok]] at [[Perimeter Institute]] concedes that theorists are disheartened at that situation, and that they are at a crossroad in theoretical (and particle) physics, calling it a deep crisis. He described the LHC results as "simple, yet extremely puzzling" and said "we have to get people to try to find the new principles that will explain the simplicity".<ref>[http://www2.macleans.ca/2013/09/05/perimeter-institute-and-the-crisis-in-modern-physics/ Perimeter Institute and the crisis in modern physics] Paul Wells, 5 Sep 2013</ref>


<small>(duodecimal)</small> 100,000 + 20,000 + 3,000 + 400 + 50 + 6 + 0.7 + 0.08 = <small>(decimal)</small> 248,832 + 41,472 + 5,184 + 576 + 60 + 6 + 0.58{{overline|3}}333333333... + 0.0{{overline|5}}5555555555...
== Applications ==


Now, because the summands are already converted to base ten, the usual decimal arithmetic is used to perform the addition and recompose the number, arriving at the conversion result:
=== Extension of possible symmetry groups ===
One reason that physicists explored supersymmetry is because it offers an extension to the more familiar symmetries of quantum field theory. These symmetries are grouped into the [[Poincaré group]] and internal symmetries and the [[Coleman–Mandula theorem]] showed that under certain assumptions, the symmetries of the [[S-matrix]] must be a direct product of the Poincaré group with a [[Compact space|compact]] internal symmetry group or if there is no [[mass gap]], the [[conformal group]] with a compact internal symmetry group.
In 1971 Golfand and Likhtman were the first to show that the Poincaré algebra can be extended through introduction of four
anticommuting spinor generators (in four dimensions), which later became known as supercharges.
In 1975 the [[Haag-Lopuszanski-Sohnius theorem]]
analyzed all possible superalgebras in the general form, including those with an extended number of the supergenerators and [[central charge]]s.
This extended super-Poincaré algebra paved the way for obtaining a very large and important class of supersymmetric field theories.


Duodecimal  ----->  Decimal
==== The supersymmetry algebra ====
{{Main|Supersymmetry algebra}}
  100,000    =   248,832
Traditional symmetries in physics are generated by objects that transform under the [[tensor]] [[representations of Lie groups|representations]] of the [[Poincaré group]] and internal symmetries. Supersymmetries, on the other hand, are generated by objects that transform under the [[spinor]] representations. According to the [[spin-statistics theorem]], [[boson]]ic fields [[commutative operation|commute]] while [[fermion]]ic fields [[anticommutativity|anticommute]]. Combining the two kinds of fields into a single [[Lie algebra|algebra]] requires the introduction of a [[graded algebra|'''Z'''<sub>2</sub>-grading]] under which the bosons are the even elements and the fermions are the odd elements. Such an algebra is called a [[Lie superalgebra]].
    20,000    =     41,472
 
    3,000    =     5,184
The simplest supersymmetric extension of the [[Poincaré algebra]] is the [[Super-Poincaré algebra]]. Expressed in terms of two [[Weyl spinor]]s, has the following [[commutator|anti-commutation]] relation:
      400    =       576
:<math>\{ Q_{ \alpha }, \bar{Q_{ \dot{ \beta }}} \} = 2( \sigma{}^{\mu} )_{ \alpha \dot{ \beta }} P_{\mu} </math>
        50    =         60
and all other anti-commutation relations between the ''Q''s and commutation relations between the ''Q''s and ''P''s vanish. In the above expression <math> P_{\mu} = -i \partial{}_{\mu}</math> are the generators of translation and <math>\sigma{}^{\mu}</math> are the [[Pauli matrices]].
  +      6    =   +      6
        0.7  =          0.58{{overline|3}}333333333...
        0.08  =         0.0{{overline|5}}5555555555...
--------------------------------------------
  123,456.78  =   296,130.63{{overline|8}}888888888...


That is, <small>(duodecimal)</small> 123,456.78 equals <small>(decimal)</small> 296,130.63{{overline|8}} ≈ 296,130.64
There are [[representation of a Lie superalgebra|representations of a Lie superalgebra]] that are analogous to representations of a Lie algebra. Each Lie algebra has an associated Lie group and a Lie superalgebra can sometimes be extended into representations of a [[Lie supergroup]].


If the given number is in decimal and the target base is duodecimal, the method is basically same. Using the digit conversion tables:
=== The Supersymmetric Standard Model ===
{{Main|Minimal Supersymmetric Standard Model}}
Incorporating supersymmetry into the [[Standard Model]] requires doubling the number of particles since there is no way that any of the particles in the Standard Model can be [[superpartner]]s of each other.  With the addition of new particles, there are many possible new interactions. The simplest possible supersymmetric model consistent with the Standard Model is the [[Minimal Supersymmetric Standard Model]] (MSSM) which can include the necessary additional new particles that are able to be [[superpartner]]s of those in the [[Standard Model]].
[[Image:Hqmc-vector.svg|thumb|300px|right|Cancellation of the [[Higgs boson]] quadratic [[mass renormalization]] between [[fermion]]ic [[top quark]] loop and [[scalar field|scalar]] stop [[squark]] [[tadpole (physics)|tadpole]] [[Feynman diagram]]s in a supersymmetric extension of the [[Standard Model]]]]


<small>(decimal)</small> 100,000 + 20,000 + 3,000 + 400 + 50 + 6 + 0.7 + 0.08 = <small>(duodecimal)</small> 49,ᘔ54 + Ɛ,6ᘔ8 + 1,8ᘔ0 + 294 + 42 + 6 + 0.8{{overline|4972}}4972497249724972497... + 0.{{overline|0Ɛ62ᘔ68781Ɛ05915343ᘔ}}0Ɛ62...
One of the main motivations for SUSY comes from the quadratically divergent contributions to the Higgs mass squared. The quantum mechanical interactions of the Higgs boson causes a large renormalization of the Higgs mass and unless there is an accidental cancellation, the natural size of the Higgs mass is the highest scale possible.   This problem is known as the [[hierarchy problem]]. Supersymmetry reduces the size of the quantum corrections by having automatic cancellations between fermionic and bosonic Higgs interactions.   If supersymmetry is restored at the weak scale, then the Higgs mass is related to supersymmetry breaking which can be induced from small non-perturbative effects explaining the vastly different scales in the weak interactions and gravitational interactions.


However, in order to do this sum and recompose the number, now the addition tables for the duodecimal system have to be used, instead of the addition tables for decimal most people are already familiar with, because the summands are now in base twelve and so the arithmetic with them has to be in duodecimal as well. In decimal, 6 + 6 equals 12, but in duodecimal it equals 10; so, if using decimal arithmetic with duodecimal numbers one would arrive at an incorrect result. Doing the arithmetic properly in duodecimal, one gets the result:
In many supersymmetric Standard Models there is a heavy stable particle (such as [[neutralino]]) which could serve as a [[Weakly interacting massive particle]] (WIMP) [[dark matter]] candidate.  The existence of a supersymmetric dark matter candidate is closely tied to [[R-parity]].


  Decimal  ----->  Duodecimal
The standard paradigm for incorporating supersymmetry into a realistic theory is to have the underlying dynamics of the theory be supersymmetric, but the ground state of the theory does not respect the symmetry and supersymmetry is [[spontaneous symmetry breaking|broken spontaneously]]. The supersymmetry break can not be done permanently by the particles of the MSSM as they currently appear. This means that there is a new sector of the theory that is responsible for the breakingThe only constraint on this new sector is that it must break supersymmetry permanently and must give superparticles TeV scale massesThere are many models that can do this and most of their details do not matterIn order to parameterize the relevant features of supersymmetry breaking, arbitrary [[soft SUSY breaking]] terms are added to the theory which temporarily break SUSY explicitly but could never arise from a complete theory of supersymmetry breaking.
   
  100,000    =    49,ᘔ54
    20,000    =      Ɛ,6ᘔ8
    3,000    =      1,8ᘔ0
      400    =        294
        50    =        42
  +      6    =  +      6
        0.7  =          0.8{{overline|4972}}4972497249724972497...
        0.08 =          0.{{overline|0Ɛ62ᘔ68781Ɛ05915343ᘔ}}0Ɛ62...
  --------------------------------------------------------
  123,456.78 =    5Ɛ,540.9{{overline|43ᘔ0Ɛ62ᘔ68781Ɛ059153}}43ᘔ...


That is, <small>(decimal)</small> 123,456.78 equals <small>(duodecimal)</small> 5Ɛ,540.9{{overline|43ᘔ0Ɛ62ᘔ68781Ɛ059153}}... ≈ 5Ɛ,540.94
==== Gauge Coupling Unification ====
{{Main|Minimal_Supersymmetric_Standard_Model#Gauge_Coupling_Unification}}
One piece of evidence for supersymmetry existing is gauge coupling unification.
The [[renormalization group]] evolution of the three gauge [[coupling constant]]s of the [[Standard Model]] is somewhat sensitive to the present particle content of the theory.  These coupling constants do not quite meet together at a common energy scale if we run the renormalization group using the [[Standard Model]].<ref name="GKane">Gordon L. Kane, ''The Dawn of Physics Beyond the Standard Model'', [[Scientific American]], June 2003, page 60 and ''The frontiers of physics'', special edition, Vol 15, #3, page 8</ref> With the addition of minimal SUSY joint convergence of the coupling constants is projected at approximately 10<sup>16</sup> [[GeV]].<ref name="GKane"/>


=== Duodecimal to decimal digit conversion ===
=== Supersymmetric quantum mechanics ===
{|class="wikitable"
{{Main|Supersymmetric quantum mechanics}}
|-
''Supersymmetric quantum mechanics'' adds the SUSY superalgebra to [[quantum mechanics]] as opposed to [[quantum field theory]]. Supersymmetric quantum mechanics often comes up when studying the dynamics of supersymmetric [[solitons]] and due to the simplified nature of having fields only functions of time (rather than space-time), a great deal of progress has been made in this subject and is now studied in its own right.
| style="background:silver;"| '''''Duod.'''''
| ''Dec.''
| style="background:silver;"| '''''Duod.'''''
| ''Dec.''
| style="background:silver;"| '''''Duod.'''''
| ''Dec.''
| style="background:silver;"| '''''Duod.'''''
| ''Dec.''
| style="background:silver;"| '''''Duod.'''''
| ''Dec.''
| style="background:silver;"| '''''Duod.'''''
| ''Dec.''
| style="background:silver;"| '''''Duod.'''''
| ''Dec.''
| style="background:silver;"| '''''Duod.'''''
| ''Dec.''
|-
| style="background:silver;"| '''100,000'''
| 248,832
| style="background:silver;"| '''10,000'''
| 20,736
| style="background:silver;"| '''1,000'''
| 1,728
| style="background:silver;"| '''100'''
| 144
| style="background:silver;"| '''10'''
| 12
| style="background:silver;"| '''1'''
| 1
| style="background:silver;"| '''0.1'''
| 0.08{{overline|3}}
| style="background:silver;"| '''0.01'''
| 0.0069{{overline|4}}
|-
| style="background:silver;"| '''200,000'''
| 497,664
| style="background:silver;"| '''20,000'''
| 41,472
| style="background:silver;"| '''2,000'''
| 3,456
| style="background:silver;"| '''200'''
| 288
| style="background:silver;"| '''20'''
| 24
| style="background:silver;"| '''2'''
| 2
| style="background:silver;"| '''0.2'''
| 0.1{{overline|6}}
| style="background:silver;"| '''0.02'''
| 0.013{{overline|8}}
|-
| style="background:silver;"| '''300,000'''
| 746,496
| style="background:silver;"| '''30,000'''
| 62,208
| style="background:silver;"| '''3,000'''
| 5,184
| style="background:silver;"| '''300'''
| 432
| style="background:silver;"| '''30'''
| 36
| style="background:silver;"| '''3'''
| 3
| style="background:silver;"| '''0.3'''
| 0.25
| style="background:silver;"| '''0.03'''
| 0.0208{{overline|3}}
|-
| style="background:silver;"| '''400,000'''
| 995,328
| style="background:silver;"| '''40,000'''
| 82,944
| style="background:silver;"| '''4,000'''
| 6,912
| style="background:silver;"| '''400'''
| 576
| style="background:silver;"| '''40'''
| 48
| style="background:silver;"| '''4'''
| 4
| style="background:silver;"| '''0.4'''
| 0.{{overline|3}}
| style="background:silver;"| '''0.04'''
| 0.02{{overline|7}}
|-
| style="background:silver;"| '''500,000'''
| 1,244,160
| style="background:silver;"| '''50,000'''
| 103,680
| style="background:silver;"| '''5,000'''
| 8,640
| style="background:silver;"| '''500'''
| 720
| style="background:silver;"| '''50'''
| 60
| style="background:silver;"| '''5'''
| 5
| style="background:silver;"| '''0.5'''
| 0.41{{overline|6}}
| style="background:silver;"| '''0.05'''
| 0.0347{{overline|2}}
|-
| style="background:silver;"| '''600,000'''
| 1,492,992
| style="background:silver;"| '''60,000'''
| 124,416
| style="background:silver;"| '''6,000'''
| 10,368
| style="background:silver;"| '''600'''
| 864
| style="background:silver;"| '''60'''
| 72
| style="background:silver;"| '''6'''
| 6
| style="background:silver;"| '''0.6'''
| 0.5
| style="background:silver;"| '''0.06'''
| 0.041{{overline|6}}
|-
| style="background:silver;"| '''700,000'''
| 1,741,824
| style="background:silver;"| '''70,000'''
| 145,152
| style="background:silver;"| '''7,000'''
| 12,096
| style="background:silver;"| '''700'''
| 1008
| style="background:silver;"| '''70'''
| 84
| style="background:silver;"| '''7'''
| 7
| style="background:silver;"| '''0.7'''
| 0.58{{overline|3}}
| style="background:silver;"| '''0.07'''
| 0.0486{{overline|1}}
|-
| style="background:silver;"| '''800,000'''
| 1,990,656
| style="background:silver;"| '''80,000'''
| 165,888
| style="background:silver;"| '''8,000'''
| 13,824
| style="background:silver;"| '''800'''
| 1152
| style="background:silver;"| '''80'''
| 96
| style="background:silver;"| '''8'''
| 8
| style="background:silver;"| '''0.8'''
| 0.{{overline|6}}
| style="background:silver;"| '''0.08'''
| 0.0{{overline|5}}
|-
| style="background:silver;"| '''900,000'''
| 2,239,488
| style="background:silver;"| '''90,000'''
| 186,624
| style="background:silver;"| '''9,000'''
| 15,552
| style="background:silver;"| '''900'''
| 1,296
| style="background:silver;"| '''90'''
| 108
| style="background:silver;"| '''9'''
| 9
| style="background:silver;"| '''0.9'''
| 0.75
| style="background:silver;"| '''0.09'''
| 0.0625
|-
| style="background:silver;"| '''ᘔ00,000'''
| 2,488,320
| style="background:silver;"| '''ᘔ0,000'''
| 207,360
| style="background:silver;"| '''ᘔ,000'''
| 17,280
| style="background:silver;"| '''ᘔ00'''
| 1,440
| style="background:silver;"| '''ᘔ0'''
| 120
| style="background:silver;"| '''ᘔ'''
| 10
| style="background:silver;"| '''0.ᘔ'''
| 0.8{{overline|3}}
| style="background:silver;"| '''0.0ᘔ'''
| 0.069{{overline|4}}
|-
| style="background:silver;"| '''Ɛ00,000'''
| 2,737,152
| style="background:silver;"| '''Ɛ0,000'''
| 228,096
| style="background:silver;"| '''Ɛ,000'''
| 19,008
| style="background:silver;"| '''Ɛ00'''
| 1,584
| style="background:silver;"| '''Ɛ0'''
| 132
| style="background:silver;"| '''Ɛ'''
| 11
| style="background:silver;"| '''0.Ɛ'''
| 0.91{{overline|6}}
| style="background:silver;"| '''0.0Ɛ'''
| 0.0763{{overline|8}}
|}


=== Decimal to duodecimal digit conversion ===
SUSY quantum mechanics involves pairs of [[Hamiltonian (quantum mechanics)|Hamiltonians]] which share a particular mathematical relationship, which are called ''partner Hamiltonians''. (The [[potential energy]] terms which occur in the Hamiltonians are then called ''partner potentials''.)  An introductory theorem shows that for every [[eigenstate]] of one Hamiltonian, its partner Hamiltonian has a corresponding eigenstate with the same energy. This fact can be exploited to deduce many properties of the eigenstate spectrum. It is analogous to the original description of SUSY, which referred to bosons and fermions. We can imagine a "bosonic Hamiltonian", whose eigenstates are the various bosons of our theory. The SUSY partner of this Hamiltonian would be "fermionic", and its eigenstates would be the theory's fermions. Each boson would have a fermionic partner of equal energy.
{|class="wikitable"
|-
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
|-
| style="background:silver;"| '''100,000'''
| 49,ᘔ54
| style="background:silver;"| '''10,000'''
| 5,954
| style="background:silver;"| '''1,000'''
| 6Ɛ4
| style="background:silver;"| '''100'''
| 84
| style="background:silver;"| '''10'''
| ᘔ
| style="background:silver;"| '''1'''
| 1
| style="background:silver;"| '''0.1'''
| 0.1{{overline|2497}}
| style="background:silver;"| '''0.01'''
| 0.0{{overline|15343ᘔ0Ɛ62ᘔ68781Ɛ059}}
|-
| style="background:silver;"| '''200,000'''
| 97,8ᘔ8
| style="background:silver;"| '''20,000'''
| Ɛ,6ᘔ8
| style="background:silver;"| '''2,000'''
| 1,1ᘔ8
| style="background:silver;"| '''200'''
| 148
| style="background:silver;"| '''20'''
| 18
| style="background:silver;"| '''2'''
| 2
| style="background:silver;"| '''0.2'''
| 0.{{overline|2497}}
| style="background:silver;"| '''0.02'''
| 0.0{{overline|2ᘔ68781Ɛ05915343ᘔ0Ɛ6}}
|-
| style="background:silver;"| '''300,000'''
| 125,740
| style="background:silver;"| '''30,000'''
| 15,440
| style="background:silver;"| '''3,000'''
| 1,8ᘔ0
| style="background:silver;"| '''300'''
| 210
| style="background:silver;"| '''30'''
| 26
| style="background:silver;"| '''3'''
| 3
| style="background:silver;"| '''0.3'''
| 0.3{{overline|7249}}
| style="background:silver;"| '''0.03'''
| 0.0{{overline|43ᘔ0Ɛ62ᘔ68781Ɛ059153}}
|-
| style="background:silver;"| '''400,000'''
| 173,594
| style="background:silver;"| '''40,000'''
| 1Ɛ,194
| style="background:silver;"| '''4,000'''
| 2,394
| style="background:silver;"| '''400'''
| 294
| style="background:silver;"| '''40'''
| 34
| style="background:silver;"| '''4'''
| 4
| style="background:silver;"| '''0.4'''
| 0.{{overline|4972}}
| style="background:silver;"| '''0.04'''
| 0.0{{overline|5915343ᘔ0Ɛ62ᘔ68781Ɛ0}}
|-
| style="background:silver;"| '''500,000'''
| 201,428
| style="background:silver;"| '''50,000'''
| 24,Ɛ28
| style="background:silver;"| '''5,000'''
| 2,ᘔ88
| style="background:silver;"| '''500'''
| 358
| style="background:silver;"| '''50'''
| 42
| style="background:silver;"| '''5'''
| 5
| style="background:silver;"| '''0.5'''
| 0.6
| style="background:silver;"| '''0.05'''
| 0.0{{overline|7249}}
|-
| style="background:silver;"| '''600,000'''
| 24Ɛ,280
| style="background:silver;"| '''60,000'''
| 2ᘔ,880
| style="background:silver;"| '''6,000'''
| 3,580
| style="background:silver;"| '''600'''
| 420
| style="background:silver;"| '''60'''
| 50
| style="background:silver;"| '''6'''
| 6
| style="background:silver;"| '''0.6'''
| 0.{{overline|7249}}
| style="background:silver;"| '''0.06'''
| 0.0{{overline|8781Ɛ05915343ᘔ0Ɛ62ᘔ6}}
|-
| style="background:silver;"| '''700,000'''
| 299,114
| style="background:silver;"| '''70,000'''
| 34,614
| style="background:silver;"| '''7,000'''
| 4,074
| style="background:silver;"| '''700'''
| 4ᘔ4
| style="background:silver;"| '''70'''
| 5ᘔ
| style="background:silver;"| '''7'''
| 7
| style="background:silver;"| '''0.7'''
| 0.8{{overline|4972}}
| style="background:silver;"| '''0.07'''
| 0.0{{overline|ᘔ0Ɛ62ᘔ68781Ɛ05915343}}
|-
| style="background:silver;"| '''800,000'''
| 326,Ɛ68
| style="background:silver;"| '''80,000'''
| 3ᘔ,368
| style="background:silver;"| '''8,000'''
| 4,768
| style="background:silver;"| '''800'''
| 568
| style="background:silver;"| '''80'''
| 68
| style="background:silver;"| '''8'''
| 8
| style="background:silver;"| '''0.8'''
| 0.{{overline|9724}}
| style="background:silver;"| '''0.08'''
| 0.{{overline|0Ɛ62ᘔ68781Ɛ05915343ᘔ}}
|-
| style="background:silver;"| '''900,000'''
| 374,ᘔ00
| style="background:silver;"| '''90,000'''
| 44,100
| style="background:silver;"| '''9,000'''
| 5,260
| style="background:silver;"| '''900'''
| 630
| style="background:silver;"| '''90'''
| 76
| style="background:silver;"| '''9'''
| 9
| style="background:silver;"| '''0.9'''
| 0.ᘔ{{overline|9724}}
| style="background:silver;"| '''0.09'''
| 0.1{{overline|0Ɛ62ᘔ68781Ɛ05915343ᘔ}}
|}


=== Conversion of powers ===
=== Supersymmetry: Applications to condensed matter physics ===
{|class="wikitable"
|-
| rowspan="2" | ''Exponent''
| colspan="2" | b=2
| colspan="2" | b=3
| colspan="2" | b=4
| colspan="2" | b=5
| colspan="2" | b=6
| colspan="2" | b=7
|-
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
|-
| b<sup>6</sup>
| style="background:silver;"| '''64'''
| 54
| style="background:silver;"| '''729'''
| 509
| style="background:silver;"| '''4,096'''
| 2454
| style="background:silver;"| '''15,625'''
| 9,061
| style="background:silver;"| '''46,656'''
| 23,000
| style="background:silver;"| '''117,649'''
| 58,101
|-
| b<sup>5</sup>
| style="background:silver;"| '''32'''
| 28
| style="background:silver;"| '''243'''
| 183
| style="background:silver;"| '''1,024'''
| 714
| style="background:silver;"| '''3,125'''
| 1,985
| style="background:silver;"| '''7,776'''
| 4,600
| style="background:silver;"| '''16,807'''
| 9,887
|-
| b<sup>4</sup>
| style="background:silver;"| '''16'''
| 14
| style="background:silver;"| '''81'''
| 69
| style="background:silver;"| '''256'''
| 194
| style="background:silver;"| '''625'''
| 441
| style="background:silver;"| '''1,296'''
| 900
| style="background:silver;"| '''2,401'''
| 1,481
|-
| b<sup>3</sup>
| style="background:silver;"| '''8'''
| 8
| style="background:silver;"| '''27'''
| 23
| style="background:silver;"| '''64'''
| 54
| style="background:silver;"| '''125'''
| ᘔ5
| style="background:silver;"| '''216'''
| 160
| style="background:silver;"| '''343'''
| 247
|-
| b<sup>2</sup>
| style="background:silver;"| '''4'''
| 4
| style="background:silver;"| '''9'''
| 9
| style="background:silver;"| '''16'''
| 14
| style="background:silver;"| '''25'''
| 21
| style="background:silver;"| '''36'''
| 30
| style="background:silver;"| '''49'''
| 41
|-
| b<sup>1</sup>
| style="background:silver;"| '''2'''
| 2
| style="background:silver;"| '''3'''
| 3
| style="background:silver;"| '''4'''
| 4
| style="background:silver;"| '''5'''
| 5
| style="background:silver;"| '''6'''
| 6
| style="background:silver;"| '''7'''
| 7
|-
| b<sup>−1</sup>
| style="background:silver;"| '''0.5'''
| 0.6
| style="background:silver;"| '''0.{{overline|3}}'''
| 0.4
| style="background:silver;"| '''0.25'''
| 0.3
| style="background:silver;"| '''0.2'''
| 0.{{overline|2497}}
| style="background:silver;"| '''0.1{{overline|6}}'''
| 0.2
| style="background:silver;"| '''0.{{overline|142857}}'''
| 0.{{overline|186ᘔ35}}
|-
| b<sup>−2</sup>
| style="background:silver;"| '''0.25'''
| 0.3
| style="background:silver;"| '''0.{{overline|1}}'''
| 0.14
| style="background:silver;"| '''0.0625'''
| 0.09
| style="background:silver;"| '''0.04'''
| 0.{{overline|05915343ᘔ0<br />Ɛ62ᘔ68781Ɛ}}
| style="background:silver;"| '''0.02{{overline|7}}'''
| 0.04
| style="background:silver;"| '''0.{{overline|0204081632653<br />06122448979591<br />836734693877551}}'''
| 0.{{overline|02Ɛ322547ᘔ05ᘔ<br />644ᘔ9380Ɛ908996<br />741Ɛ615771283Ɛ}}
|}


{|class="wikitable"
SUSY concepts have provided useful extensions to the [[WKB approximation]].  In addition, SUSY has been applied to disorder averaged systems both quantum and non-quantum (through [[statistical mechanics]]). The [[Fokker-Planck equation]] being an example of a non-quantum theory. The `supersymmetry' in all these systems arises from the fact that one is modelling one particle and as such the`statistics' don't matter. The use of the supersymmetry method provides a mathematical rigorous alternative to the [[replica trick]], but only in non-interacting systems, which attempts to address the so-called `problem of the denominator' under disorder averaging. For more on the applications of supersymmetry in [[condensed matter physics]] see the book<ref>''Supersymmetry in Disorder and Chaos'', Konstantin Efetov, Cambridge university press, 1997.</ref>
|-
| rowspan="2" | ''Exponent''
| colspan="2" | b=8
| colspan="2" | b=9
| colspan="2" | '''b=10'''
| colspan="2" | b=11
| colspan="2" | '''b=12'''
|-
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
| style="background:silver;"| '''''Dec.'''''
| ''Duod.''
|-
| b<sup>6</sup>
| style="background:silver;"| '''262,144'''
| 107,854
| style="background:silver;"| '''531,441'''
| 217,669
| style="background:silver;"| '''1,000,000'''
| 402,854
| style="background:silver;"| '''1,771,561'''
| 715,261
| style="background:silver;"| '''2,985,984'''
| 1,000,000
|-
| b<sup>5</sup>
| style="background:silver;"| '''32,768'''
| 16,Ɛ68
| style="background:silver;"| '''59,049'''
| 2ᘔ,209
| style="background:silver;"| '''100,000'''
| 49,ᘔ54
| style="background:silver;"| '''161,051'''
| 79,24Ɛ
| style="background:silver;"| '''248,832'''
| 100,000
|-
| b<sup>4</sup>
| style="background:silver;"| '''4,096'''
| 2,454
| style="background:silver;"| '''6,561'''
| 3,969
| style="background:silver;"| '''10,000'''
| 5,954
| style="background:silver;"| '''14,641'''
| 8,581
| style="background:silver;"| '''20,736'''
| 10,000
|-
| b<sup>3</sup>
| style="background:silver;"| '''512'''
| 368
| style="background:silver;"| '''729'''
| 509
| style="background:silver;"| '''1,000'''
| 6Ɛ4
| style="background:silver;"| '''1,331'''
| 92Ɛ
| style="background:silver;"| '''1,728'''
| 1,000
|-
| b<sup>2</sup>
| style="background:silver;"| '''64'''
| 54
| style="background:silver;"| '''81'''
| 69
| style="background:silver;"| '''100'''
| 84
| style="background:silver;"| '''121'''
| ᘔ1
| style="background:silver;"| '''144'''
| 100
|-
| b<sup>1</sup>
| style="background:silver;"| '''8'''
| 8
| style="background:silver;"| '''9'''
| 9
| style="background:silver;"| '''10'''
| ᘔ
| style="background:silver;"| '''11'''
| Ɛ
| style="background:silver;"| '''12'''
| 10
|-
| b<sup>−1</sup>
| style="background:silver;"| '''0.125'''
| 0.16
| style="background:silver;"| '''0.{{overline|1}}'''
| 0.14
| style="background:silver;"| '''0.1'''
| 0.1{{overline|2497}}
| style="background:silver;"| '''0.{{overline|09}}'''
| 0.{{overline|1}}
| style="background:silver;"| '''0.08{{overline|3}}'''
| 0.1
|-
| b<sup>−2</sup>
| style="background:silver;"| '''0.015625'''
| 0.023
| style="background:silver;"| '''0.{{overline|012345679}}'''
| 0.0194
| style="background:silver;"| '''0.01'''
| 0.0{{overline|15343ᘔ0Ɛ6<br />2ᘔ68781Ɛ059}}
| style="background:silver;"| '''0.{{overline|00826446280<br />99173553719}}'''
| 0.{{overline|0123456789Ɛ}}
| style="background:silver;"| '''0.0069{{overline|4}}'''
| 0.01
|}


==Fractions and irrational numbers==
=== Mathematics ===
===Fractions===
SUSY is also sometimes studied mathematically for its intrinsic properties. This is because it describes complex fields satisfying a property known as [[holomorphy]], which allows holomorphic quantities to be exactly computed. This makes supersymmetric models useful [[toy model]]s of more realistic theories.  A prime example of this has been the demonstration of S-duality in four-dimensional gauge theories<ref name="krasnitz02">
Duodecimal [[Fraction (mathematics)|fractions]] may be simple:
{{cite book
* {{frac|2}} = 0.6
| last =Krasnitz
* {{frac|3}} = 0.4
| first =Michael
* {{frac|4}} = 0.3
| title =Correlation functions in supersymmetric gauge theories from supergravity fluctuations
* {{frac|6}} = 0.2
| publisher = Princeton University Department of Physics
* {{frac|8}} = 0.16
| year = 2002
* {{frac|9}} = 0.14
| location = Princeton University Department of Physics
| pages =91
| url =http://www.princeton.edu/physics/graduate-program/theses/theses-from-2002/MKrasnitzthesis.pdf
}}
</ref> that interchanges particles and [[Magnetic monopole|monopoles]].


or complicated
The proof of the [[Atiyah-Singer index theorem]] is much simplified by the use of supersymmetric quantum mechanics.
* {{frac|5}}  = 0.24972497... recurring (easily rounded to 0.25)
* {{frac|7}}  = 0.186ᘔ35186ᘔ35... recurring (easily rounded to 0.187)
* {{frac|ᘔ}}  = 0.124972497... recurring (rounded to 0.125)
* {{frac|Ɛ}}  = 0.11111... recurring (rounded to 0.11)
* {{frac|11}} = 0.0Ɛ0Ɛ... recurring (rounded to 0.0Ɛ)


{|class="wikitable"
== General supersymmetry ==
|-
| ''Examples in duodecimal''
| ''Decimal equivalent''
|-
| 1 × ({{frac|5|8}}) = 0.76
| 1 × ({{frac|5|8}}) = 0.625
|-
| 100 × ({{frac|5|8}}) = 76
| 144 × ({{frac|5|8}}) = 90
|-
| {{frac|576|9}} = 76
| {{frac|810|9}} = 90
|-
| {{frac|400|9}} = 54
| {{frac|576|9}} = 64
|-
| 1ᘔ.6 + 7.6 = 26
| 22.5 + 7.5 = 30
|}


As explained in [[recurring decimal]]s, whenever an [[irreducible fraction]] is written in [[radix point]] notation in any base, the fraction can be expressed exactly (terminates) if and only if all the [[prime factor]]s of its denominator are also prime factors of the base. Thus, in base-ten (=&nbsp;2×5) system, fractions whose denominators are made up solely of multiples of 2 and 5 terminate: {{frac|8}}&nbsp;=&nbsp;{{frac|(2×2×2)}}, {{frac|20}}&nbsp;=&nbsp;{{frac|(2×2×5)}} and {{frac|500}}&nbsp;=&nbsp;{{frac|(2×2×5×5×5)}} can be expressed exactly as 0.125, 0.05 and 0.002 respectively. {{frac|3}} and {{frac|7}}, however, recur (0.333... and 0.142857142857...). In the duodecimal (=&nbsp;2×2×3) system, {{frac|8}} is exact; {{frac|20}} and {{frac|500}} recur because they include 5 as a factor; {{frac|3}} is exact; and {{frac|7}} recurs, just as it does in decimal.
Supersymmetry appears in many different contexts in theoretical physics that are closely relatedIt is possible to have multiple supersymmetries and also have supersymmetric extra dimensions.


=== Recurring digits ===
=== Extended supersymmetry ===
Arguably, factors of 3 are more commonly encountered in real-life [[division (mathematics)|division]] problems than factors of 5 (or would be, were it not for the decimal system having influenced most cultures). Thus, in practical applications, the nuisance of [[recurring decimals]] is encountered less often when duodecimal notation is used. Advocates of duodecimal systems argue that this is particularly true of financial calculations, in which the twelve months of the year often enter into calculations.
{{Main|Extended supersymmetry}}
It is possible to have more than one kind of supersymmetry transformation.  Theories with more than one supersymmetry transformation are known as [[extended supersymmetry|extended supersymmetric]] theories.  The more supersymmetry a theory has, the more constrained the field content and interactions are. Typically the number of copies of a supersymmetry is a power of 2, i.e. 1, 2, 4, 8.   In four dimensions, a spinor has four degrees of freedom and thus the minimal number of supersymmetry generators is four in four dimensions and having eight copies of supersymmetry means that there are 32 supersymmetry generators.


However, when recurring fractions ''do'' occur in duodecimal notation, they are less likely to have a very short period than in decimal notation, because [[12 (number)|12]] (twelve) is between two [[prime number]]s, [[11 (number)|11]] (eleven) and [[13 (number)|13]] (thirteen), whereas ten is adjacent to [[composite number]] [[9 (number)|9]]. Nonetheless, having a shorter or longer period doesn't help the main inconvenience that one does not get a finite representation for such fractions in the given base (so [[rounding]], which introduces inexactitude, is necessary to handle them in calculations), and overall one is more likely to have to deal with infinite recurring digits when fractions are expressed in decimal than in duodecimal, because one out of every three consecutive numbers contains the prime factor [[3 (number)|3]] in its factorization, whereas only one out of every five contains the prime factor [[5 (number)|5]]. All other prime factors, except 2, are not shared by either ten or twelve, so they do not
The maximal number of supersymmetry generators possible is 32. Theories with more than 32 supersymmetry generators automatically have massless fields with spin greater than 2.  It is not known how to make massless fields with spin greater than two interact, so the maximal number of supersymmetry generators considered is 32.   This corresponds to an ''N'' = 8 supersymmetry theory. Theories with 32 supersymmetries automatically have a [[graviton]].
influence the relative likeliness of encountering recurring digits (any irreducible fraction that contains any of these other factors in its denominator will recur in either base). Also, the prime factor [[2 (number)|2]] appears twice in the factorization of twelve, whereas only once in the factorization of ten; which means that most fractions whose denominators are [[power of two|powers of two]] will have a shorter, more convenient terminating representation in dozenal than in decimal (e.g., 1/(2<sup>2</sup>) = 0.25 <SMALL>dec</SMALL> = 0.3 <SMALL>doz</SMALL>; 1/(2<sup>3</sup>) = 0.125 <SMALL>dec</SMALL> = 0.16 <SMALL>doz</SMALL>; 1/(2<sup>4</sup>) = 0.0625 <SMALL>dec</SMALL> = 0.09 <SMALL>doz</SMALL>; 1/(2<sup>5</sup>) = 0.03125 <SMALL>dec</SMALL> = 0.046 <SMALL>doz</SMALL>; etc.).


Values in '''bold''' indicate that value is exact.
In four dimensions there are the following theories, with the corresponding multiplets<ref>Polchinski,J. ''String theory. Vol. 2: Superstring theory and beyond'', Appendix B
</ref>(CPT adds a copy, whenever they are not invariant under such symmetry)
* ''N'' = 1
Chiral multiplet:
(0,{{frac|1|2}})
Vector multiplet:
({{frac|1|2}},1)
Gravitino multiplet:
(1,{{frac|3|2}})
Graviton multiplet:
({{frac|3|2}},2)
* ''N'' = 2
hypermultiplet:
(-{{frac|1|2}},0<sup>2</sup>,{{frac|1|2}})
vector multiplet:
(0,{{frac|1|2}}<sup>2</sup>,1)
supergravity multiplet:
(1,{{frac|3|2}}<sup>2</sup>,2)
* ''N'' = 4
Vector multiplet:
(-1,-{{frac|1|2}}<sup>4</sup>,0<sup>6</sup>,{{frac|1|2}}<sup>4</sup>,1)
Supergravity multiplet:
(0,{{frac|1|2}}<sup>4</sup>,1<sup>6</sup>,{{frac|3|2}}<sup>4</sup>,2)


{|class="wikitable"
* ''N'' = 8
|- style="text-align:center;"
Supergravity multiplet:
| colspan="3"| Decimal base<br><SMALL>Prime factors of the base: <span style="color:Green">'''2'''</span>, <span style="color:Green">'''5'''</span></SMALL><br><SMALL>Prime factors of one below the base: <span style="color:Blue">'''3'''</span></SMALL><br><SMALL>Prime factors of one above the base: <span style="color:Orange">'''11'''</span></SMALL>
(-2,-{{frac|3|2}}<sup>8</sup>,-1<sup>28</sup>,-{{frac|1|2}}<sup>56</sup>,0<sup>70</sup>,{{frac|1|2}}<sup>56</sup>,1<sup>28</sup>,{{frac|3|2}}<sup>8</sup>,2)
| colspan="3"| '''Duodecimal / Dozenal base'''<br><SMALL>Prime factors of the base: <span style="color:Green">'''2'''</span>, <span style="color:Green">'''3'''</span></SMALL><br><SMALL>Prime factors of one below the base: <span style="color:Blue">'''Ɛ'''</span></SMALL><br><SMALL>Prime factors of one above the base: <span style="color:Orange">'''11'''</span></SMALL>
|- style="text-align:center;"
|| Fraction
|| <SMALL>Prime factors<br>of the denominator<SMALL>
|| Positional representation
|| Positional representation
|| <SMALL>Prime factors<br>of the denominator<SMALL>
|| Fraction
|-
| style="text-align:center;"| 1/2
| style="text-align:center;"| <span style="color:Green">'''2'''</span>
| '''0.5'''
| '''0.6'''
| style="text-align:center;"| <span style="color:Green">'''2'''</span>
| style="text-align:center;"| 1/2
|-
| style="text-align:center;"| 1/3
| style="text-align:center;"| <span style="color:Blue">'''3'''</span>
| style="background:silver;"| '''0.'''3333... = '''0.'''{{overline|3}}
| '''0.4'''
| style="text-align:center;"| <span style="color:Green">'''3'''</span>
| style="text-align:center;"| 1/3
|-
| style="text-align:center;"| 1/4
| style="text-align:center;"| <span style="color:Green">'''2'''</span>
| '''0.25'''
| '''0.3'''
| style="text-align:center;"| <span style="color:Green">'''2'''</span>
| style="text-align:center;"| 1/4
|-
| style="text-align:center;"| 1/5
| style="text-align:center;"| <span style="color:Green">'''5'''</span>
| '''0.2'''
| style="background:silver;"| '''0.'''24972497... = '''0.'''{{overline|2497}}
| style="text-align:center;"| <span style="color:Red">'''5'''</span>
| style="text-align:center;"| 1/5
|-
| style="text-align:center;"| 1/6
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Blue">'''3'''</span>
| style="background:silver;"| '''0.1'''{{overline|6}}
| '''0.2'''
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Green">'''3'''</span>
| style="text-align:center;"| 1/6
|-
| style="text-align:center;"| 1/7
| style="text-align:center;"| <span style="color:Red">'''7'''</span>
| style="background:silver;"| '''0.'''{{overline|142857}}
| style="background:silver;"| '''0.'''{{overline|186ᘔ35}}
| style="text-align:center;"| <span style="color:Red">'''7'''</span>
| style="text-align:center;"| 1/7
|-
| style="text-align:center;"| 1/8
| style="text-align:center;"| <span style="color:Green">'''2'''</span>
| '''0.125'''
| '''0.16'''
| style="text-align:center;"| <span style="color:Green">'''2'''</span>
| style="text-align:center;"| 1/8
|-
| style="text-align:center;"| 1/9
| style="text-align:center;"| <span style="color:Blue">'''3'''</span>
| style="background:silver;"| '''0.'''{{overline|1}}
| '''0.14'''
| style="text-align:center;"| <span style="color:Green">'''3'''</span>
| style="text-align:center;"| 1/9
|-
| style="text-align:center;"| 1/10
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Green">'''5'''</span>
| '''0.1'''
| style="background:silver;"| '''0.1'''{{overline|2497}}
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Red">'''5'''</span>
| style="text-align:center;"| 1/ᘔ
|-
| style="text-align:center;"| 1/11
| style="text-align:center;"| <span style="color:Orange">'''11'''</span>
| style="background:silver;"| '''0.'''{{overline|09}}
| style="background:silver;"| '''0.'''{{overline|1}}
| style="text-align:center;"| <span style="color:Blue">'''Ɛ'''</span>
| style="text-align:center;"| 1/Ɛ
|-
| style="text-align:center;"| 1/12
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Blue">'''3'''</span>
| style="background:silver;"| '''0.08'''{{overline|3}}
| '''0.1'''
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Green">'''3'''</span>
| style="text-align:center;"| 1/10
|-
| style="text-align:center;"| 1/13
| style="text-align:center;"| <span style="color:Red">'''13'''</span>
| style="background:silver;"| '''0.'''{{overline|076923}}
| style="background:silver;"| '''0.'''{{overline|0Ɛ}}
| style="text-align:center;"| <span style="color:Orange">'''11'''</span>
| style="text-align:center;"| 1/11
|-
| style="text-align:center;"| 1/14
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Red">'''7'''</span>
| style="background:silver;"| '''0.0'''{{overline|714285}}
| style="background:silver;"| '''0.0'''{{overline|ᘔ35186}}
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Red">'''7'''</span>
| style="text-align:center;"| 1/12
|-
| style="text-align:center;"| 1/15
| style="text-align:center;"| <span style="color:Blue">'''3'''</span>, <span style="color:Green">'''5'''</span>
| style="background:silver;"| '''0.0'''{{overline|6}}
| style="background:silver;"| '''0.0'''{{overline|9724}}
| style="text-align:center;"| <span style="color:Green">'''3'''</span>, <span style="color:Red">'''5'''</span>
| style="text-align:center;"| 1/13
|-
| style="text-align:center;"| 1/16
| style="text-align:center;"| <span style="color:Green">'''2'''</span>
| '''0.0625'''
| '''0.09'''
| style="text-align:center;"| <span style="color:Green">'''2'''</span>
| style="text-align:center;"| 1/14
|-
| style="text-align:center;"| 1/17
| style="text-align:center;"| <span style="color:Red">'''17'''</span>
| style="background:silver;"| '''0.'''{{overline|0588235294117647}}
| style="background:silver;"| '''0.'''{{overline|08579214Ɛ36429ᘔ7}}
| style="text-align:center;"| <span style="color:Red">'''15'''</span>
| style="text-align:center;"| 1/15
|-
| style="text-align:center;"| 1/18
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Blue">'''3'''</span>
| style="background:silver;"| '''0.0'''{{overline|5}}
| '''0.08'''
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Green">'''3'''</span>
| style="text-align:center;"| 1/16
|-
| style="text-align:center;"| 1/19
| style="text-align:center;"| <span style="color:Red">'''19'''</span>
| style="background:silver;"| '''0.'''{{overline|052631578947368421}}
| style="background:silver;"| '''0.'''{{overline|076Ɛ45}}
| style="text-align:center;"| <span style="color:Red">'''17'''</span>
| style="text-align:center;"| 1/17
|-
| style="text-align:center;"| 1/20
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Green">'''5'''</span>
| '''0.05'''
| style="background:silver;"| '''0.0'''{{overline|7249}}
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Red">'''5'''</span>
| style="text-align:center;"| 1/18
|-
| style="text-align:center;"| 1/21
| style="text-align:center;"| <span style="color:Blue">'''3'''</span>, <span style="color:Red">'''7'''</span>
| style="background:silver;"| '''0.'''{{overline|047619}}
| style="background:silver;"| '''0.0'''{{overline|6ᘔ3518}}
| style="text-align:center;"| <span style="color:Green">'''3'''</span>, <span style="color:Red">'''7'''</span>
| style="text-align:center;"| 1/19
|-
| style="text-align:center;"| 1/22
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Orange">'''11'''</span>
| style="background:silver;"| '''0.0'''{{overline|45}}
| style="background:silver;"| '''0.0'''{{overline|6}}
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Blue">'''Ɛ'''</span>
| style="text-align:center;"| 1/1ᘔ
|-
| style="text-align:center;"| 1/23
| style="text-align:center;"| <span style="color:Red">'''23'''</span>
| style="background:silver;"| '''0.'''{{overline|0434782608695652173913}}
| style="background:silver;"| '''0.'''{{overline|06316948421}}
| style="text-align:center;"| <span style="color:Red">'''1Ɛ'''</span>
| style="text-align:center;"| 1/1Ɛ
|-
| style="text-align:center;"| 1/24
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Blue">'''3'''</span>
| style="background:silver;"| '''0.041'''{{overline|6}}
| '''0.06'''
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Green">'''3'''</span>
| style="text-align:center;"| 1/20
|-
| style="text-align:center;"| 1/25
| style="text-align:center;"| <span style="color:Green">'''5'''</span>
| '''0.04'''
| style="background:silver;"| '''0.'''{{overline|05915343ᘔ0Ɛ62ᘔ68781Ɛ}}
| style="text-align:center;"| <span style="color:Red">'''5'''</span>
| style="text-align:center;"| 1/21
|-
| style="text-align:center;"| 1/26
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Red">'''13'''</span>
| style="background:silver;"| '''0.0'''{{overline|384615}}
| style="background:silver;"| '''0.0'''{{overline|56}}
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Orange">'''11'''</span>
| style="text-align:center;"| 1/22
|-
| style="text-align:center;"| 1/27
| style="text-align:center;"| <span style="color:Blue">'''3'''</span>
| style="background:silver;"| '''0.'''{{overline|037}}
| '''0.054'''
| style="text-align:center;"| <span style="color:Green">'''3'''</span>
| style="text-align:center;"| 1/23
|-
| style="text-align:center;"| 1/28
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Red">'''7'''</span>
| style="background:silver;"| '''0.03'''{{overline|571428}}
| style="background:silver;"| '''0.0'''{{overline|5186ᘔ3}}
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Red">'''7'''</span>
| style="text-align:center;"| 1/24
|-
| style="text-align:center;"| 1/29
| style="text-align:center;"| <span style="color:Red">'''29'''</span>
| style="background:silver;"| '''0.'''{{overline|0344827586206896551724137931}}
| style="background:silver;"| '''0.'''{{overline|04Ɛ7}}
| style="text-align:center;"| <span style="color:Red">'''25'''</span>
| style="text-align:center;"| 1/25
|-
| style="text-align:center;"| 1/30
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Blue">'''3'''</span>, <span style="color:Green">'''5'''</span>
| style="background:silver;"| '''0.0'''{{overline|3}}
| style="background:silver;"| '''0.0'''{{overline|4972}}
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Green">'''3'''</span>, <span style="color:Red">'''5'''</span>
| style="text-align:center;"| 1/26
|-
| style="text-align:center;"| 1/31
| style="text-align:center;"| <span style="color:Red">'''31'''</span>
| style="background:silver;"| '''0.'''{{overline|032258064516129}}
| style="background:silver;"| '''0.'''{{overline|0478ᘔᘔ093598166Ɛ74311Ɛ28623ᘔ55}}
| style="text-align:center;"| <span style="color:Red">'''27'''</span>
| style="text-align:center;"| 1/27
|-
| style="text-align:center;"| 1/32
| style="text-align:center;"| <span style="color:Green">'''2'''</span>
| '''0.03125'''
| '''0.046'''
| style="text-align:center;"| <span style="color:Green">'''2'''</span>
| style="text-align:center;"| 1/28
|-
| style="text-align:center;"| 1/33
| style="text-align:center;"| <span style="color:Blue">'''3'''</span>, <span style="color:Orange">'''11'''</span>
| style="background:silver;"| '''0.'''{{overline|03}}
| style="background:silver;"| '''0.0'''{{overline|4}}
| style="text-align:center;"| <span style="color:Green">'''3'''</span>, <span style="color:Blue">'''Ɛ'''</span>
| style="text-align:center;"| 1/29
|-
| style="text-align:center;"| 1/34
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Red">'''17'''</span>
| style="background:silver;"| '''0.0'''{{overline|2941176470588235}}
| style="background:silver;"| '''0.0'''{{overline|429ᘔ708579214Ɛ36}}
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Red">'''15'''</span>
| style="text-align:center;"| 1/2ᘔ
|-
| style="text-align:center;"| 1/35
| style="text-align:center;"| <span style="color:Green">'''5'''</span>, <span style="color:Red">'''7'''</span>
| style="background:silver;"| '''0.0'''{{overline|285714}}
| style="background:silver;"| '''0.'''{{overline|0414559Ɛ3931}}
| style="text-align:center;"| <span style="color:Red">'''5'''</span>, <span style="color:Red">'''7'''</span>
| style="text-align:center;"| 1/2Ɛ
|-
| style="text-align:center;"| 1/36
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Blue">'''3'''</span>
| style="background:silver;"| '''0.02'''{{overline|7}}
| '''0.04'''
| style="text-align:center;"| <span style="color:Green">'''2'''</span>, <span style="color:Green">'''3'''</span>
| style="text-align:center;"| 1/30
|}


=== Irrational numbers ===
=== Supersymmetry in alternate numbers of dimensions ===
As for [[irrational number]]s, none of them have a finite representation in ''any'' of the [[rational number|rational]]-based positional number systems (such as the decimal and duodecimal ones); this is because a rational-based positional number system is essentially nothing but a way of expressing quantities as a sum of fractions whose denominators are powers of the base, and by definition no ''finite'' sum of rational numbers can ever result in an irrational number. For example, 123.456 = 1 × 1/10<sup>−2</sup> + 2 × 1/10<sup>−1</sup> + 3 × 1/10<sup>0</sup> + 4 × 1/10<sup>1</sup> + 5 × 1/10<sup>2</sup> + 6 × 1/10<sup>3</sup> (this is also the reason why fractions that contain prime factors in their denominator not in common with those of the base do not have a terminating representation in that base). Moreover, the infinite series of digits of an irrational number does not exhibit a pattern of repetition; instead, the different digits succeed in a seemingly random fashion. The following chart compares the first few digits of the decimal and duodecimal representation of several of the most important [[algebraic number|algebraic]] and [[transcendental number|transcendental]] irrational numbers. Some of these numbers may be perceived as having fortuitous patterns, making them easier to memorize, when represented in one base or the other.


{|class="wikitable"
It is possible to have supersymmetry in dimensions other than four.  Because the properties of spinors change drastically between different dimensions, each dimension has its characteristic.  In ''d'' dimensions, the size of spinors is roughly 2<sup>''d''/2</sup> or 2<sup>(''d''&nbsp;−&nbsp;1)/2</sup>. Since the maximum number of supersymmetries is 32, the greatest number of dimensions in which a supersymmetric theory can exist is eleven.
|- style="text-align:center;"
|| ''Algebraic irrational number''
|| In decimal
|| '''In duodecimal / dozenal'''
|-
| style="text-align:center;"| [[Square root of 2|√2]] <SMALL>(the length of the [[diagonal]] of a unit [[Square (geometry)|square]])</SMALL>
| 1.41421356237309... (≈ 1.4142)
| 1.4Ɛ79170ᘔ07Ɛ857... (≈ 1.5)
|-
| style="text-align:center;"| [[Square root of 3|√3]] <SMALL>(the length of the diagonal of a unit [[cube]], or twice the [[height]] of an [[equilateral triangle]] of unit side)</SMALL>
| 1.73205080756887... (≈ 1.732)
| 1.894Ɛ97ƐƐ968704... (≈ 1.895)
|-
| style="text-align:center;"| [[Square root of 5|√5]] <SMALL>(the length of the [[diagonal]] of a 1×2 [[rectangle]])</SMALL>
| 2.2360679774997... (≈ 2.236)
| 2.29ƐƐ132540589... (≈ 2.2ᘔ)
|-
| style="text-align:center;"| [[Golden ratio|φ]] <SMALL>(phi, the golden ratio = <math>\scriptstyle \frac{1+\sqrt{5}}{2}</math>)</SMALL>
| 1.6180339887498... (≈ 1.618)
| 1.74ƐƐ6772802ᘔ4... (≈ 1.75)
|- style="text-align:center;"
|| ''Transcendental irrational number''
|| In decimal
|| '''In duodecimal / dozenal'''
|-
| style="text-align:center;"| ''[[Pi|π]]'' <SMALL>(pi, the ratio of [[circumference]] to [[diameter]])<SMALL>
| 3.1415926535897932384626433<br />8327950288419716939937510...<br />(≈ 3.1416)
| 3.184809493Ɛ918664573ᘔ6211Ɛ<br />Ɛ151551ᘔ05729290ᘔ7809ᘔ492...<br />(≈ 3.1848)
|-
| style="text-align:center;"| [[E (mathematical constant)|e]] <SMALL>(the base of the [[natural logarithm]])</SMALL>
| 2.718281828459045... (≈ 2.718)
| 2.8752360698219Ɛ8... (≈ 2.875)
|}


The first few digits of the decimal and dozenal representation of another important number, the [[Euler–Mascheroni constant]] (the status of which as a rational or irrational number is not yet known), are:
== Supersymmetry as a quantum group ==
{{Main|Supersymmetry as a quantum group}}
Supersymmetry can be reinterpreted in the language of [[noncommutative geometry]] and [[quantum group]]s. In particular, it involves a mild form of noncommutativity, namely [[supercommutativity]]. See the main article for more details.


{|class="wikitable"
== Supersymmetry in quantum gravity ==
|- style="text-align:center;"
Supersymmetry is part of a larger enterprise of theoretical physics to unify everything we know about the physical world into a single fundamental framework of physical laws, known as the quest for a [[Theory of Everything]] (TOE).  A significant part of this larger enterprise is the quest for a theory of [[quantum gravity]], which would unify the classical theory of [[general relativity]] and the [[Standard Model]], which explains the other [[fundamental interaction|three basic forces]] in physics ([[electromagnetism]], the [[strong interaction]], and the [[weak interaction]]), and provides a palette of [[fundamental particle]]s upon which all four forces act. Two of the most active approaches to forming a theory of quantum gravity are [[string theory]] and [[loop quantum gravity]] (LQG), although in theory, supersymmetry could be a component of other theoretical approaches as well.
|| ''Number''
|| In decimal
|| '''In duodecimal / dozenal'''
|-
| style="text-align:center;"| [[Euler–Mascheroni constant|γ]] <SMALL>(the limiting difference between the [[harmonic series (mathematics)|harmonic series]] and the natural logarithm)</SMALL>
| 0.57721566490153... (~ 0.577)
| 0.6Ɛ15188ᘔ6760Ɛ3... (~ 0.7)
|}


==Advocacy and "dozenalism"==
For [[string theory]] to be consistent, supersymmetry appears to be required at some level (although it may be a strongly broken symmetry). In particle theory, supersymmetry is recognized as a way to stabilize the [[hierarchy problem|hierarchy]] between the unification scale and the electroweak scale (or the [[Higgs boson]] mass), and can also provide a natural [[dark matter]] candidate. String theory also requires extra spatial dimensions which have to be compactified as in [[Kaluza-Klein theory]].
The case for the duodecimal system was put forth at length in F. Emerson Andrews' 1935 book ''New Numbers: How Acceptance of a Duodecimal Base Would Simplify Mathematics''. Emerson noted that, due to the prevalence of factors of twelve in many traditional units of weight and measure, many of the computational advantages claimed for the metric system could be realized ''either'' by the adoption of ten-based weights and measure ''or'' by the adoption of the duodecimal number system.


Rather than the symbols "A" for ten and "B" for eleven as used in [[hexadecimal]] notation and [[vigesimal]] notation (or "T" and "E" for ten and eleven), he suggested in his book and used a script X and a script E, <math>x\!</math> ([[Unicode|U+]]1D4B3) and [[Image:Scripte.png]] (U+2130), to represent the digits ten and eleven respectively, because, at least on a page of Roman script, these characters were distinct from any existing letters or numerals, yet were readily available in printers' fonts. He chose <math>x\!</math> for its resemblance to the Roman numeral X, and [[Image:Scripte.png]] as the first letter of the word "eleven".
[[Loop quantum gravity]] (LQG) predicts no additional spatial dimensions, nor anything else about particle physics. These theories can be formulated in three spatial dimensions and one dimension of time, although in some LQG theories dimensionality is an [[emergent property]] of the theory, rather than a fundamental assumption of the theory. Also, LQG is a theory of quantum gravity which does not require supersymmetry. [[Lee Smolin]], one of the originators of LQG, has proposed that a loop quantum gravity theory incorporating either supersymmetry or extra dimensions, or both, be called "loop quantum gravity II".


Another popular notation, introduced by Sir [[Isaac Pitman]], is to use a rotated 2 (ᘔ) (resembling a script ''τ'' for "ten") to represent ten and a rotated or horizontally flipped 3 (Ɛ) (which again resembles ''ε'') to represent eleven. This is the convention commonly employed by the Dozenal Society of Great Britain and has the advantage of being easily recognizable as digits because of their resemblance in shape to existing digits. On the other hand, the Dozenal Society of America adopted for some years the convention of using an [[asterisk]] * for ten and a [[Number sign|hash]] # for eleven. The reason was that the symbol * resembles a struck-through X, whereas the symbol # resembles a doubly-struck-through 11, and both symbols are already present in [[telephone]] [[Rotary dial|dials]]. However, critics pointed out these symbols do not look anything like digits. Some other systems write 10 as Φ (a combination of 1 and 0) and eleven as a cross of two lines (+, x, or † for example)<!-- "+" is similar to the Chinese character for ten & "X" is the Roman numeral for ten. -->.
If experimental evidence confirms supersymmetry in the form of [[supersymmetric particle]]s such as the [[neutralino]] that is often believed to be the lightest [[superpartner]], some people believe this would be a major boost to [[string theory]]. Since supersymmetry is a required component of string theory, any discovered supersymmetry would be consistent with string theory. If the [[Large Hadron Collider]] and other major particle physics experiments fail to detect supersymmetric partners or evidence of extra dimensions, many versions of [[string theory]] which had predicted certain low mass superpartners to existing particles may need to be significantly revised. The failure of experiments to discover either supersymmetric partners or extra spatial dimensions, {{As of|2013|lc=on}}, has encouraged [[loop quantum gravity]] researchers.


Problems with these symbols are evident, most notably that most of them can not be represented in the [[seven-segment display]] of most [[calculator]] displays ([[Image:Scripte.png]] being an exception, although "E" is used on calculators to indicate an [[error message]]). However, 10 and 11 do fit, both within a single digit (11 fits as is, whereas the 10 has to be tilted sideways, resulting in a character that resembles an O with a [[macron]], ō or <u>o</u>). A and B also fit (although B must be represented as lowercase "b" and as such, 6 must have a bar over it to distinguish the two figures) and are used on calculators for bases higher than ten.
== Current status ==
Supersymmetric models are constrained by a variety of experiments, including measurements of low-energy observables, for example the [[anomalous magnetic moment of the muon]] at [[Brookhaven National Laboratory|Brookhaven]]; the [[WMAP]] dark matter density measurement and direct detection experiments, for example [[XENON]]-100; and by particle collider experiments, including [[B-physics]], Higgs phenomenology and direct searches for superpartners (sparticles), at the [[Large Electron–Positron Collider]], [[Tevatron]] and the [[LHC]].


In "Little Twelvetoes", American television series ''[[Schoolhouse Rock!]]'' portrayed an alien child using base-twelve arithmetic, using "dek", "el" and "doh" as names for ten, eleven and twelve, and Andrews' script-X and script-E for the digit symbols. ("Dek" is from the prefix "deca", "el" being short for "eleven" and "doh" an apparent shortening of "dozen".)<ref>[http://www.schoolhouserock.tv/Little.html "Little Twelvetoes"]{{dead link|date=January 2014}}</ref>
Historically, the tightest limits were from direct production at colliders. The first mass limits for squarks and gluinos were made at [[CERN]] by the [[UA1 experiment]] and the [[UA2 experiment]] at the [[Super Proton Synchrotron]]. LEP later set very strong limits.<ref>LEPSUSYWG, ALEPH, DELPHI, L3 and OPAL experiments, charginos, large m0 LEPSUSYWG/01-03.1</ref> In 2006 these limits were extended by the D0 experiment.<ref>{{cite paper |author=The D0-Collaboration |title=Search for associated production of charginos and neutralinos in the trilepton final state using 2.3 fb<sup>−1</sup> of data |year=2009 |arxiv=0901.0646 }}</ref><ref>{{cite paper |author=The D0 Collaboration |title=Search for squarks and gluinos in events with jets and missing transverse energy in <math>p\bar{p}</math> collisions at <math>\sqrt{s}</math>=1.96 TeV |arxiv=0712.3805 |year=2006 }}</ref>


The Dozenal Society of America and the Dozenal Society of Great Britain promote widespread adoption of the base-twelve system. They use the word "dozenal" instead of "duodecimal" because the latter comes from Latin roots that express twelve in base-ten terminology.
From 2003, [[WMAP]]'s [[dark matter]] density measurements have strongly constrained supersymmetry models, which have to be tuned to invoke a particular mechanism to sufficiently reduce the [[neutralino]] density.


The renowned mathematician and mental calculator [[Alexander Aitken|Alexander Craig Aitken]] was an outspoken advocate of the advantages and superiority of duodecimal over decimal:
Prior to the launch of the LHC, in 2009, fits of available data to CMSSM and NUHM1 indicated that squarks and gluinos were most likely to have masses in 500 to 800 GeV range, though values as high as 2.5 TeV were allowed with low probabilities. Neutralinos and sleptons were expected to be quite light, with the lightest neutralino and the lightest stau most likely to be found between 100 to 150 GeV.<ref>{{cite journal|url=http://xxx.lanl.gov/pdf/0907.5568v1.pdf|title=Likelihood Functions for Supersymmetric Observables in Frequentist Analyses of the CMSSM and NUHM1|author=O. Buchmueller et al.}}</ref>
{{quote|The duodecimal tables are easy to master, easier than the decimal ones; and in elementary teaching they would be so much more interesting, since young children would find more fascinating things to do with twelve rods or blocks than with ten. Anyone having these tables at command will do these calculations more than one-and-a-half times as fast in the duodecimal scale as in the decimal. This is my experience; I am certain that even more so it would be the experience of others.|A. C. Aitken|in ''The Listener'', January 25, 1962<ref>[http://www.dozenalsociety.org.uk/leafletsetc/aitken.html Basic Stuff<!-- Bot generated title -->]{{dead link|date=January 2014}}</ref>}}


{{quote|But the final quantitative advantage, in my own experience, is this: in varied and extensive calculations of an ordinary and not unduly complicated kind, carried out over many years, I come to the conclusion that the efficiency of the decimal system might be rated at about 65 or less, if we assign 100 to the duodecimal.|A. C. Aitken|''The Case Against Decimalisation'' (Edinburgh / London: Oliver & Boyd, 1962)<ref>[http://www.dozenalsociety.org.uk/pdfs/aitken.pdf The Case against Decimalisation<!-- Bot generated title -->]</ref>}}
As of 2012, the [[LHC]] has found no evidence for supersymmetry, and, as a result, has surpassed existing experimental limits from [[Large Electron–Positron Collider]] and [[Tevatron]] and partially excluded the aforementioned expected ranges.<ref>[http://www.math.columbia.edu/~woit/wordpress/?p=3479 Implications of Initial LHC Searches for Supersymmetry]</ref><ref>[http://arxiv.org/abs/1101.4664 Fine-tuning implications for complementary dark matter and LHC SUSY searches]</ref><ref>[http://resonaances.blogspot.com/2011/02/what-lhc-tells-about-susy.html What LHC tells about SUSY]</ref><ref>[http://www.hep.ph.ic.ac.uk/susytalks/iop-susytapper.pdf Early SUSY searches at the LHC]</ref> Based on the data sample collected by the CMS detector at the LHC through the summer of 2011, [[Minimal Supersymmetric Standard Model|CMSSM]] squarks have been excluded up to the mass of 1.1 TeV and gluinos have been excluded up to 500 GeV.<ref>{{cite journal|title=Search for Supersymmetry at the LHC in Events with Jets and Missing Transverse Energy|author=CMS Collaboration|journal=Physical Review Letters|date=November 2011|doi=10.1103/PhysRevLett.107.221804|last2=Khachatryan|first2=V.|last3=Sirunyan|first3=A.|last4=Tumasyan|first4=A.|last5=Adam|first5=W.|last6=Bergauer|first6=T.|last7=Dragicevic|first7=M.|last8=Erö|first8=J.|last9=Fabjan|first9=C.|volume=107|issue=22|last1000=Andreev|first1000=Yu|last1001=Dermenev|first1001=A|last1002=Gninenko|first1002=S|last1003=Golubev|first1003=N|last1004=Kirsanov|first1004=M|last1005=Krasnikov|first1005=N|last1006=Matveev|first1006=V|last1007=Pashenkov|first1007=A|last1008=Toropin|first1008=A|last1009=Troitsky|first1009=S|last2000=Baumgartel|first2000=D|last2001=Boeriu|first2001=O|last2002=Chasco|first2002=M|last2003=Reucroft|first2003=S|last2004=Swain|first2004=J|last2005=Trocino|first2005=D|last2006=Wood|first2006=D|last2007=Zhang|first2007=J|last2008=Anastassov|first2008=A|last2009=Kubik|first2009=A}}</ref> Searches are only applicable for a finite set of tested points because simulation using the [[Monte Carlo method]] must be made so that limits for that particular model can be calculated. This complicates matters because different experiments have looked at different sets of points. Some extrapolation between points can be made within particular models but it is difficult to set general limits even for the [[Minimal Supersymmetric Standard Model]].


In [[Leo Frankowski]]'s [[Conrad Stargard]] novels, Conrad introduces a duodecimal system of arithmetic at the suggestion of a merchant, who is accustomed to buying and selling goods in dozens and grosses, rather than tens or hundreds. He then invents an entire system of weights and measures in base twelve, including a clock with twelve hours in a day, rather than twenty-four hours.
In 2011 and 2012, the [[LHC]] discovered a [[Higgs boson]] with a mass of about 125 GeV, and with couplings to fermions and bosons which are consistent with the [[Standard Model]]. The MSSM predicts that the mass of the lightest [[Higgs boson]] should not be much higher than the mass of the [[Z boson]], and, in the absence of [[fine tuning]] (with the supersymmetry breaking scale on the order of 1 TeV), should not exceed 130 GeV. Furthermore, for values of the MSSM parameter ''tan'' β ≤ 3, it predicts Higgs mass below 114 GeV over most of the parameter space.<ref>{{cite journal|title=Higgs Boson Theory and Phenomenology|author=Marcela Carena and Howard E. Haber|arxiv=hep-ph/0208209v3.pdf|year=1970|bibcode=2003PrPNP..50...63C|last2=Haber|volume=50|pages=63|journal=Progress in Particle and Nuclear Physics|doi=10.1016/S0146-6410(02)00177-1}}</ref> This region of Higgs mass was excluded by [[LEP]] by 2000. The [[LHC]] result is somewhat problematic for the minimal supersymmetric model, as the value of 125 GeV is relatively large for the model and can only be achieved with large radiative loop corrections from top [[squarks]], which many theorists consider to be "unnatural" (see [[naturalness]] and [[fine tuning]]).<ref>{{cite journal|title=Implications of a 125 GeV Higgs for the MSSM and Low-Scale SUSY Breaking|author=Patrick Draper et al|date=December 2011|arxiv=1112.3068}}</ref> Furthermore, in 2012, the [[LHC]] measured deviations from [[Standard Model]] predicted [[Higgs boson|Higgs]] couplings, particularly in their gamma-gamma final state, which, if they persist, could severely constrain the MSSM.


In [[Lee Carroll]]'s ''Kryon: Alchemy of the Human Spirit'', a chapter is dedicated to the advantages of the duodecimal system. The duodecimal system is supposedly suggested by [[Kryon]] (one of the widely popular [[New Age]] channeled entities) for all-round use, aiming at better and more natural representation of nature of the Universe through mathematics. An individual article "Mathematica" by James D. Watt (included in the above publication) exposes a few of the unusual symmetry connections between the duodecimal system and the [[golden ratio]], as well as provides numerous number symmetry-based arguments for the universal nature of the base-12 number system.<ref>''[https://www.kryon.com/k_13.html Kryon—Alchemy of the Human Spirit]'', ISBN 0-9636304-8-2</ref>
A summary listed eight arguments against supersymmetry.<ref>"Eight Arguments Against Supersymmetry" http://www.physicsforums.com/showthread.php?t=727664</ref> (1) The LUX experiment for cold dark matter has not observed neutralinos. (2) The large size of the WMAP cold spot is larger than predicted by Lambda cold dark matter models. (3) The large-scale flow of galaxies is larger than predicted by Lambda CDM models. (4) The number of faint dwarf galaxies is smaller than predicted by Lambda CDM models. (5) Neither the ATLAS nor the CMS collaboration have observed gluinos and squarks. (6) The rest mass, interaction cross-section and decay rates of the Higgs boson are compatible with the standard theory, but not with earlier predictions by supersymmetric models. (7) Dirac fermions can be described by a gravitation theory which includes Cartan torsion (Einstein-Cartan theory), supersymmetry is not required. (8) The mass hierarchy problem of Grand Unified theories need not arise if Grand Unification does not exist. The proton decay predicted by Grand Unified theories has not been observed. The quantization of electric charge can be explained by theories which include Dirac magnetic monopoles, so Grand Unification is not necessary.


=== Dozenal clock ===
In spite of the null searches and the heavy Higgs, a recent analysis of the constrained minimal supersymmetric Standard Model, the [[CMSSM]], suggests that the model is still compatible with all present experimental constraints.<ref>[http://arxiv.org/abs/1212.2636]"Global Fits of the cMSSM and NUHM including the LHC Higgs discovery and new XENON100 constraints", C. Strege, G. Bertone, F. Feroz, M. Fornasa, R. Ruiz de Austri, R. Trotta, arXiv:1212.2636</ref> The preferred masses for squarks and gluinos is about 2 TeV. The resulting fine-tuning of the [[Higgs boson]] mass (see [[little hierarchy problem]]) and [[Z-boson]] mass (see [[mu problem]]), however, is considered "unnatural," and some theorists now favor extended supersymmetry models, for example, the [[NMSSM]].
* [http://www.dozenalsociety.org.uk/apps/dozenalclock.html Dozenal Clock by Joshua Harkey]
* [http://dozenal.ae-web.ca/ Dozenal Clock with four hands in several variants by Paul Rapoport]
* [http://www.gingerbill.org/dozenal/demo.html Dozenal Clock by Bill Hall]


=== Dozenal metric systems ===
== See also ==
[[Systems of measurement]] proposed by dozenalists include:
<div style="-moz-column-count:2; column-count:2;">
* Tom Pendlebury's [[TGM (measurement system)|TGM]] system<ref>{{cite web|last=Pendlebury|first=Tom|title=TGM|url=http://www.dozenalsociety.org.uk/pdfs/TGMbooklet.pdf}}</ref>
* [[Supersymmetric gauge theory]]
* Takashi Suga's [[Universal Unit System]]<ref>{{cite web|last=Suga|first=Takashi|title=Universal Unit System|url=http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/}}</ref>
* [[Wess–Zumino model]]
* [[Minimal Supersymmetric Standard Model]]
* [[Supersymmetry as a quantum group]]
* [[Quantum group#Quantum groups and non-commutative geometry|Quantum group]]
* [[Supercharge]]
* [[Superfield]]
* [[Supergeometry]]
* [[Supergravity]]
* [[Supergroup (physics)|Supergroup]]
* [[Superspace]]


== Duodecimal digits on computerized writing systems ==
</div>
{{Symb|[[File:Duodecimal-digit-ten-Dozenal-Society-of-Great-Britain.svg]] [[File:Duodecimal-digit-eleven-Dozenal-Society-of-Great-Britain.svg]] · [[File:Duodecimal-digit-ten-Dozenal-Society-of-America.svg]] [[File:Duodecimal-digit-eleven-Dozenal-Society-of-America.svg]]}}
In March 2013, a proposal was submitted to include the digits for ten and eleven propagated by the Dozenal Societies of Great Britain and America in [[Unicode]].<ref name="N4399">{{Internetquelle|autor=Karl Pentzlin|hrsg=ISO/IEC JTC1/SC2/WG2, Document N4399|titel=Proposal to encode Duodecimal Digit Forms in the UCS|url=http://std.dkuug.dk/jtc1/sc2/wg2/docs/n4399.pdf |datum=2013-03-30|zugriff=2013-06-29|sprache=en|format=PDF}}</ref> In June 2013, this was partially accepted, advising for the British digits the provisional code points U+218A {{smallcaps|turned digit two}} and U+218B {{smallcaps|turned digit three}}.<ref>{{Internetquelle|hrsg=ISO/IEC JTC1/SC2/WG2, Document N4465|titel=Subdivision of work – Amendment 1 10646 4<sup>th</sup> edition|url=http://std.dkuug.dk/jtc1/sc2/wg2/docs/n4465.pdf |datum=2013-06-20|zugriff=2013-06-29|sprache=en|format=PDF}}</ref> By this, the actual availability as Unicode characters can be expected for 2016 (1200<sub>doz.</sub>).


Also, the turned digits two and three are available in [[LaTeX]] as <code>\textturntwo</code> and <code>\textturnthree</code>.<ref name="LATEX">{{Internetquelle
== References ==
|autor = Scott Pakin
{{Reflist|30em}}
|titel = The Comprehensive LATEX Symbol List
|url = http://www.tex.ac.uk/tex-archive/info/symbols/comprehensive/symbols-a4.pdf
|datum = 2009-11-09
|zugriff = 2013-02-04
|sprache = en
|format = PDF; 4,4&nbsp;MB
}}</ref>


== See also ==
== Further reading ==
* [[Senary]] (base 6)
[http://www.stringwiki.org/wiki/Supersymmetry_and_Supergravity Supersymmetry and Supergravity] page in [http://www.stringwiki.org/wiki/String_Theory_Wiki String Theory Wiki] lists more books and reviews.
* [[base 24|Quadrovigesimal]] (base 24)
 
* [[base 36|Sexatrigesimal]] (base 36)
=== Theoretical introductions, free and online  ===
* [[Sexagesimal]] (base 60)
* {{cite arXiv|eprint=hep-ph/9709356|title= A Supersymmetry Primer|author=S. Martin|year=2011}}
* [[Babylonian numerals]]
* {{cite arXiv|eprint=hep-th/9612114|title=Introduction to Supersymmetry|author=[[Joseph Lykken|Joseph D. Lykken]]|year=1996}}
* {{cite arXiv|eprint=hep-ph/9611409|title=An Introduction to Supersymmetry|author=Manuel Drees|year=1996}}
* {{cite arXiv|eprint=hep-th/0101055|title=Introduction to Supersymmetry|author=Adel Bilal|year=2001}}
* [http://www.physics.uc.edu/~argyres/661/susy2001.pdf An Introduction to Global Supersymmetry] by [[Philip Arygres]], 2001
 
=== Monographs ===
* [http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521857864 Weak Scale Supersymmetry] by Howard Baer and Xerxes Tata, 2006.
* Cooper, F., A. Khare and U. Sukhatme.  "Supersymmetry in Quantum Mechanics."  Phys. Rep. 251 (1995) 267-85 (arXiv:hep-th/9405029).
* Junker, G. ''Supersymmetric Methods in Quantum and Statistical Physics'', Springer-Verlag (1996).
* Gordon L. Kane.''Supersymmetry: Unveiling the Ultimate Laws of Nature'' Basic Books, New York (2001).  ISBN 0-7382-0489-7.
* Gordon L. Kane and Shifman, M., eds.  ''The Supersymmetric World: The Beginnings of the Theory,'' World Scientific, Singapore (2000).  ISBN 981-02-4522-X.
* Weinberg, Steven, ''The Quantum Theory of Fields, Volume 3: Supersymmetry'', Cambridge University Press, Cambridge, (1999). ISBN 0-521-66000-9.
* Wess, Julius, and Jonathan Bagger, ''Supersymmetry and Supergravity'', Princeton University Press, Princeton, (1992). ISBN 0-691-02530-4.
*Duplij, Steven;  Siegel, Warren; Bagger, Jonathan (eds.) (2005).  ''Concise Encyclopedia of Supersymmetry'',  Springer, Berlin/New York, (Second printing) ISBN 978-1-4020-1338-6


== References ==
=== On experiments ===
{{reflist}}
* {{cite journal | author=Bennett GW, ''et al.''; Muon (g−2) Collaboration | title=Measurement of the negative muon anomalous magnetic moment to 0.7 ppm | journal=Physical Review Letters | volume=92 | issue=16 | year=2004 | pages=161802 | pmid=15169217 | doi=10.1103/PhysRevLett.92.161802 | bibcode=2004PhRvL..92p1802B|arxiv = hep-ex/0401008 }}
* Brookhaven National Laboratory (Jan. 8, 2004). ''[http://www.bnl.gov/bnlweb/pubaf/pr/2004/bnlpr010804.htm New g−2 measurement deviates further from Standard Model].'' Press Release.
* Fermi National Accelerator Laboratory (Sept 25, 2006). ''[http://www.fnal.gov/pub/presspass/press_releases/CDF_meson.html Fermilab's CDF scientists have discovered the quick-change behavior of the B-sub-s meson.]'' Press Release.


== External links ==
== External links ==
* [http://www.dozenal.org/ Dozenal Society of America]
* [http://profmattstrassler.com/articles-and-posts/lhcposts/what-do-current-mid-august-2011-lhc-results-imply-about-supersymmetry/ What do current LHC results (mid-August 2011) imply about supersymmetry?] Matt Strassler
* [http://www.dozenalsociety.org.uk/ Dozenal Society of Great Britain website]
* [https://twiki.cern.ch/twiki/bin/view/AtlasPublic/SupersymmetryPublicResults#Early_2011_Data_5_CONF_Notes ATLAS Experiment Supersymmetry search documents]
* {{cite web|last=Grime|first=James|title=Base 12: Dozenal or Duodecimal|url=http://www.numberphile.com/videos/base_12.html|work=Numberphile|publisher=[[Brady Haran]]}}
* [https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsSUS CMS Experiment Supersymmetry search documents]
* [http://www.cosmosmagazine.com/node/714 "Particle wobble shakes up supersymmetry"], ''Cosmos'' magazine, September 2006
* [http://www.bbc.co.uk/news/science-environment-14680570 LHC results put supersymmetry theory 'on the spot'] BBC news 27/8/2011
* [http://www.bbc.co.uk/news/science-environment-20300100 SUSY running out of hiding places] BBC news 12/11/2012
 
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[[Category:Positional numeral systems]]
[[Category:Theoretical physics]]
[[Category:Concepts in physics]]
[[Category:Supersymmetry| ]]
[[Category:Physics beyond the Standard Model]]

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Template:Beyond the Standard Model In particle physics, supersymmetry (SUSY) is a proposed extension of spacetime symmetry that relates two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer spin.[1] Each particle from one group is associated with a particle from the other, called its superpartner, whose spin differs by a half-integer. In a theory with unbroken supersymmetry each pair of superpartners shares the same mass and internal quantum numbers besides spin, but since no superpartners have been observed yet, supersymmetry must be a spontaneously broken symmetryPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.. The failure of the Large Hadron Collider to find evidence for supersymmetry has led some physicists to suggest that the theory should be abandoned.[2] Experiments with the Large Hadron Collider also yielded an extremely rare particle decay event which casts doubt on supersymmetry.[3] A major weakness of SUSY is that it is not falsifiable, because its breaking mechanism and the minimum mass above which it is restored are unknown. This minimum mass can be pushed upwards to arbitrarily large values, without disproving the symmetry.

Supersymmetry differs notably from currently known symmetries in that it establishes a symmetry between classical and quantum physics, which up to now has not been observed in any other domain. While any number of bosons can occupy the same quantum state, for fermions this is not possible because of the exclusion principle, which allows only one fermion in a given state. But when the occupation numbers become large, quantum physics approaches the classical limit. This means that while bosons also exist in classical physics, fermions do not. That makes it difficult to expect that bosons, if at all, possess the same quantum numbers as fermions.[4] There is only indirect evidence for the existence of supersymmetry, primarily in the form of evidence for gauge coupling unification.[5] However this refers only to electroweak and strong interactions and does not provide the ultimate unification of all interactions, since it leaves gravitation untouched.

Supersymmetry is also motivated by solutions to several theoretical problems, for generally providing many desirable mathematical properties, and for ensuring sensible behavior at high energies. Supersymmetric quantum field theory is often much easier to analyze, as many more problems become exactly solvable. When supersymmetry is imposed as a local symmetry, Einstein's theory of general relativity is included automatically, and the result is said to be a theory of supergravity. It is also a feature of a candidate of a theory of everything, superstring theory.

A central motivation for supersymmetry close to the TeV energy scale is the resolution of the hierarchy problem of the Standard Model. Without the extra supersymmetric particles, the Higgs boson mass is subject to quantum corrections which are so large as to naturally drive it close to the Planck mass barring its fine tuning to an extraordinarily tiny value. In the supersymmetric theory, on the other hand, these quantum corrections are canceled by those from the corresponding superpartners above the supersymmetry breaking scale, which becomes the new characteristic natural scale for the Higgs mass. Other attractive features of TeV-scale supersymmetry are the fact that it often provides a candidate dark matter particle at a mass scale consistent with thermal relic abundance calculations,[6][7] provides a natural mechanism for electroweak symmetry breaking and allows for the precise high-energy unification of the weak, the strong and electromagnetic interactions. Therefore, scenarios where supersymmetric partners appear with masses not much greater than 1 TeV are considered the most well-motivated by theorists.[8] These scenarios would imply that experimental traces of the superpartners should begin to emerge in high-energy collisions at the LHC relatively soon. As of September 2011, no meaningful signs of the superpartners have been observed,[9][10] which is beginning to significantly constrain the most popular incarnations of supersymmetry. However, the total parameter space of consistent supersymmetric extensions of the Standard Model is extremely diverse and can not be definitively ruled out at the LHC.

Another theoretically appealing property of supersymmetry is that it offers the only "loophole" to the Coleman–Mandula theorem, which prohibits spacetime and internal symmetries from being combined in any nontrivial way, for quantum field theories like the Standard Model under very general assumptions. The Haag-Lopuszanski-Sohnius theorem demonstrates that supersymmetry is the only way spacetime and internal symmetries can be consistently combined.[11]

The Minimal Supersymmetric Standard Model is one of the best studied candidates for physics beyond the Standard Model.

History

A supersymmetry relating mesons and baryons was first proposed, in the context of hadronic physics, by Hironari Miyazawa in 1966. This supersymmetry did not involve spacetime, that is it concerned internal symmetry, and was badly broken. His work was largely ignored at the time.[12][13][14][15]

J. L. Gervais and B. Sakita (in 1971),[16] Yu. A. Golfand and E. P. Likhtman (also in 1971), and D.V. Volkov and V.P. Akulov (in 1972),[17] independently rediscovered supersymmetry in the context of quantum field theory, a radically new type of symmetry of spacetime and fundamental fields, which establishes a relationship between elementary particles of different quantum nature, bosons and fermions, and unifies spacetime and internal symmetries of the microscopic world. Supersymmetry with a consistent Lie-algebraic graded structure on which the Gervais−Sakita rediscovery was based directly first arose in 1971[18] in the context of an early version of string theory by Pierre Ramond, John H. Schwarz and André Neveu.

Finally, J. Wess and B. Zumino (in 1974)[19] identified the characteristic renormalization features of four dimensional supersymmetric field theories, which singled them out as remarkable QFTs, and they and Abdus Salam and their fellow researchers introduced early particle physics applications. The mathematical structure of supersymmetry (Graded Lie superalgebras) has subsequently been applied successfully to other areas of physics, in a variety of fields, ranging from nuclear physics,[20] critical phenomena,[21] quantum mechanics to statistical physics. It remains a vital part of many proposed theories of physics.

The first realistic supersymmetric version of the Standard Model was proposed in 1981 by Howard Georgi and Savas Dimopoulos and is called the Minimal Supersymmetric Standard Model or MSSM for short. It was proposed to solve the hierarchy problem and predicts superpartners with masses between 100 GeV and 1 TeV.

As of September 2011, no meaningful signs of the superpartners have been observed.[9][10] The Large Hadron Collider at CERN is producing the world's highest energy collisions and offers the best chance at discovering superparticles for the foreseeable future.

After the discovery of the Higgs particle in 2012, it was expected that supersymmetric particles would be found at CERN, but there has been still no evidence of them. The LHCb and CMS experiments at the LHC made the first definitive observation of a Strange B meson decaying into two muons, confirming a standard model prediction, but a blow for those hoping for signs of supersymmetry.[22] Neil Turok at Perimeter Institute concedes that theorists are disheartened at that situation, and that they are at a crossroad in theoretical (and particle) physics, calling it a deep crisis. He described the LHC results as "simple, yet extremely puzzling" and said "we have to get people to try to find the new principles that will explain the simplicity".[23]

Applications

Extension of possible symmetry groups

One reason that physicists explored supersymmetry is because it offers an extension to the more familiar symmetries of quantum field theory. These symmetries are grouped into the Poincaré group and internal symmetries and the Coleman–Mandula theorem showed that under certain assumptions, the symmetries of the S-matrix must be a direct product of the Poincaré group with a compact internal symmetry group or if there is no mass gap, the conformal group with a compact internal symmetry group. In 1971 Golfand and Likhtman were the first to show that the Poincaré algebra can be extended through introduction of four anticommuting spinor generators (in four dimensions), which later became known as supercharges. In 1975 the Haag-Lopuszanski-Sohnius theorem analyzed all possible superalgebras in the general form, including those with an extended number of the supergenerators and central charges. This extended super-Poincaré algebra paved the way for obtaining a very large and important class of supersymmetric field theories.

The supersymmetry algebra

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. Traditional symmetries in physics are generated by objects that transform under the tensor representations of the Poincaré group and internal symmetries. Supersymmetries, on the other hand, are generated by objects that transform under the spinor representations. According to the spin-statistics theorem, bosonic fields commute while fermionic fields anticommute. Combining the two kinds of fields into a single algebra requires the introduction of a Z2-grading under which the bosons are the even elements and the fermions are the odd elements. Such an algebra is called a Lie superalgebra.

The simplest supersymmetric extension of the Poincaré algebra is the Super-Poincaré algebra. Expressed in terms of two Weyl spinors, has the following anti-commutation relation:

and all other anti-commutation relations between the Qs and commutation relations between the Qs and Ps vanish. In the above expression are the generators of translation and are the Pauli matrices.

There are representations of a Lie superalgebra that are analogous to representations of a Lie algebra. Each Lie algebra has an associated Lie group and a Lie superalgebra can sometimes be extended into representations of a Lie supergroup.

The Supersymmetric Standard Model

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. Incorporating supersymmetry into the Standard Model requires doubling the number of particles since there is no way that any of the particles in the Standard Model can be superpartners of each other. With the addition of new particles, there are many possible new interactions. The simplest possible supersymmetric model consistent with the Standard Model is the Minimal Supersymmetric Standard Model (MSSM) which can include the necessary additional new particles that are able to be superpartners of those in the Standard Model.

Cancellation of the Higgs boson quadratic mass renormalization between fermionic top quark loop and scalar stop squark tadpole Feynman diagrams in a supersymmetric extension of the Standard Model

One of the main motivations for SUSY comes from the quadratically divergent contributions to the Higgs mass squared. The quantum mechanical interactions of the Higgs boson causes a large renormalization of the Higgs mass and unless there is an accidental cancellation, the natural size of the Higgs mass is the highest scale possible. This problem is known as the hierarchy problem. Supersymmetry reduces the size of the quantum corrections by having automatic cancellations between fermionic and bosonic Higgs interactions. If supersymmetry is restored at the weak scale, then the Higgs mass is related to supersymmetry breaking which can be induced from small non-perturbative effects explaining the vastly different scales in the weak interactions and gravitational interactions.

In many supersymmetric Standard Models there is a heavy stable particle (such as neutralino) which could serve as a Weakly interacting massive particle (WIMP) dark matter candidate. The existence of a supersymmetric dark matter candidate is closely tied to R-parity.

The standard paradigm for incorporating supersymmetry into a realistic theory is to have the underlying dynamics of the theory be supersymmetric, but the ground state of the theory does not respect the symmetry and supersymmetry is broken spontaneously. The supersymmetry break can not be done permanently by the particles of the MSSM as they currently appear. This means that there is a new sector of the theory that is responsible for the breaking. The only constraint on this new sector is that it must break supersymmetry permanently and must give superparticles TeV scale masses. There are many models that can do this and most of their details do not matter. In order to parameterize the relevant features of supersymmetry breaking, arbitrary soft SUSY breaking terms are added to the theory which temporarily break SUSY explicitly but could never arise from a complete theory of supersymmetry breaking.

Gauge Coupling Unification

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. One piece of evidence for supersymmetry existing is gauge coupling unification. The renormalization group evolution of the three gauge coupling constants of the Standard Model is somewhat sensitive to the present particle content of the theory. These coupling constants do not quite meet together at a common energy scale if we run the renormalization group using the Standard Model.[5] With the addition of minimal SUSY joint convergence of the coupling constants is projected at approximately 1016 GeV.[5]

Supersymmetric quantum mechanics

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. Supersymmetric quantum mechanics adds the SUSY superalgebra to quantum mechanics as opposed to quantum field theory. Supersymmetric quantum mechanics often comes up when studying the dynamics of supersymmetric solitons and due to the simplified nature of having fields only functions of time (rather than space-time), a great deal of progress has been made in this subject and is now studied in its own right.

SUSY quantum mechanics involves pairs of Hamiltonians which share a particular mathematical relationship, which are called partner Hamiltonians. (The potential energy terms which occur in the Hamiltonians are then called partner potentials.) An introductory theorem shows that for every eigenstate of one Hamiltonian, its partner Hamiltonian has a corresponding eigenstate with the same energy. This fact can be exploited to deduce many properties of the eigenstate spectrum. It is analogous to the original description of SUSY, which referred to bosons and fermions. We can imagine a "bosonic Hamiltonian", whose eigenstates are the various bosons of our theory. The SUSY partner of this Hamiltonian would be "fermionic", and its eigenstates would be the theory's fermions. Each boson would have a fermionic partner of equal energy.

Supersymmetry: Applications to condensed matter physics

SUSY concepts have provided useful extensions to the WKB approximation. In addition, SUSY has been applied to disorder averaged systems both quantum and non-quantum (through statistical mechanics). The Fokker-Planck equation being an example of a non-quantum theory. The `supersymmetry' in all these systems arises from the fact that one is modelling one particle and as such the`statistics' don't matter. The use of the supersymmetry method provides a mathematical rigorous alternative to the replica trick, but only in non-interacting systems, which attempts to address the so-called `problem of the denominator' under disorder averaging. For more on the applications of supersymmetry in condensed matter physics see the book[24]

Mathematics

SUSY is also sometimes studied mathematically for its intrinsic properties. This is because it describes complex fields satisfying a property known as holomorphy, which allows holomorphic quantities to be exactly computed. This makes supersymmetric models useful toy models of more realistic theories. A prime example of this has been the demonstration of S-duality in four-dimensional gauge theories[25] that interchanges particles and monopoles.

The proof of the Atiyah-Singer index theorem is much simplified by the use of supersymmetric quantum mechanics.

General supersymmetry

Supersymmetry appears in many different contexts in theoretical physics that are closely related. It is possible to have multiple supersymmetries and also have supersymmetric extra dimensions.

Extended supersymmetry

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. It is possible to have more than one kind of supersymmetry transformation. Theories with more than one supersymmetry transformation are known as extended supersymmetric theories. The more supersymmetry a theory has, the more constrained the field content and interactions are. Typically the number of copies of a supersymmetry is a power of 2, i.e. 1, 2, 4, 8. In four dimensions, a spinor has four degrees of freedom and thus the minimal number of supersymmetry generators is four in four dimensions and having eight copies of supersymmetry means that there are 32 supersymmetry generators.

The maximal number of supersymmetry generators possible is 32. Theories with more than 32 supersymmetry generators automatically have massless fields with spin greater than 2. It is not known how to make massless fields with spin greater than two interact, so the maximal number of supersymmetry generators considered is 32. This corresponds to an N = 8 supersymmetry theory. Theories with 32 supersymmetries automatically have a graviton.

In four dimensions there are the following theories, with the corresponding multiplets[26](CPT adds a copy, whenever they are not invariant under such symmetry)

  • N = 1

Chiral multiplet: (0,Template:Frac) Vector multiplet: (Template:Frac,1) Gravitino multiplet: (1,Template:Frac) Graviton multiplet: (Template:Frac,2)

  • N = 2

hypermultiplet: (-Template:Frac,02,Template:Frac) vector multiplet: (0,Template:Frac2,1) supergravity multiplet: (1,Template:Frac2,2)

  • N = 4

Vector multiplet: (-1,-Template:Frac4,06,Template:Frac4,1) Supergravity multiplet: (0,Template:Frac4,16,Template:Frac4,2)

  • N = 8

Supergravity multiplet: (-2,-Template:Frac8,-128,-Template:Frac56,070,Template:Frac56,128,Template:Frac8,2)

Supersymmetry in alternate numbers of dimensions

It is possible to have supersymmetry in dimensions other than four. Because the properties of spinors change drastically between different dimensions, each dimension has its characteristic. In d dimensions, the size of spinors is roughly 2d/2 or 2(d − 1)/2. Since the maximum number of supersymmetries is 32, the greatest number of dimensions in which a supersymmetric theory can exist is eleven.

Supersymmetry as a quantum group

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. Supersymmetry can be reinterpreted in the language of noncommutative geometry and quantum groups. In particular, it involves a mild form of noncommutativity, namely supercommutativity. See the main article for more details.

Supersymmetry in quantum gravity

Supersymmetry is part of a larger enterprise of theoretical physics to unify everything we know about the physical world into a single fundamental framework of physical laws, known as the quest for a Theory of Everything (TOE). A significant part of this larger enterprise is the quest for a theory of quantum gravity, which would unify the classical theory of general relativity and the Standard Model, which explains the other three basic forces in physics (electromagnetism, the strong interaction, and the weak interaction), and provides a palette of fundamental particles upon which all four forces act. Two of the most active approaches to forming a theory of quantum gravity are string theory and loop quantum gravity (LQG), although in theory, supersymmetry could be a component of other theoretical approaches as well.

For string theory to be consistent, supersymmetry appears to be required at some level (although it may be a strongly broken symmetry). In particle theory, supersymmetry is recognized as a way to stabilize the hierarchy between the unification scale and the electroweak scale (or the Higgs boson mass), and can also provide a natural dark matter candidate. String theory also requires extra spatial dimensions which have to be compactified as in Kaluza-Klein theory.

Loop quantum gravity (LQG) predicts no additional spatial dimensions, nor anything else about particle physics. These theories can be formulated in three spatial dimensions and one dimension of time, although in some LQG theories dimensionality is an emergent property of the theory, rather than a fundamental assumption of the theory. Also, LQG is a theory of quantum gravity which does not require supersymmetry. Lee Smolin, one of the originators of LQG, has proposed that a loop quantum gravity theory incorporating either supersymmetry or extra dimensions, or both, be called "loop quantum gravity II".

If experimental evidence confirms supersymmetry in the form of supersymmetric particles such as the neutralino that is often believed to be the lightest superpartner, some people believe this would be a major boost to string theory. Since supersymmetry is a required component of string theory, any discovered supersymmetry would be consistent with string theory. If the Large Hadron Collider and other major particle physics experiments fail to detect supersymmetric partners or evidence of extra dimensions, many versions of string theory which had predicted certain low mass superpartners to existing particles may need to be significantly revised. The failure of experiments to discover either supersymmetric partners or extra spatial dimensions, Template:As of, has encouraged loop quantum gravity researchers.

Current status

Supersymmetric models are constrained by a variety of experiments, including measurements of low-energy observables, for example the anomalous magnetic moment of the muon at Brookhaven; the WMAP dark matter density measurement and direct detection experiments, for example XENON-100; and by particle collider experiments, including B-physics, Higgs phenomenology and direct searches for superpartners (sparticles), at the Large Electron–Positron Collider, Tevatron and the LHC.

Historically, the tightest limits were from direct production at colliders. The first mass limits for squarks and gluinos were made at CERN by the UA1 experiment and the UA2 experiment at the Super Proton Synchrotron. LEP later set very strong limits.[27] In 2006 these limits were extended by the D0 experiment.[28][29]

From 2003, WMAP's dark matter density measurements have strongly constrained supersymmetry models, which have to be tuned to invoke a particular mechanism to sufficiently reduce the neutralino density.

Prior to the launch of the LHC, in 2009, fits of available data to CMSSM and NUHM1 indicated that squarks and gluinos were most likely to have masses in 500 to 800 GeV range, though values as high as 2.5 TeV were allowed with low probabilities. Neutralinos and sleptons were expected to be quite light, with the lightest neutralino and the lightest stau most likely to be found between 100 to 150 GeV.[30]

As of 2012, the LHC has found no evidence for supersymmetry, and, as a result, has surpassed existing experimental limits from Large Electron–Positron Collider and Tevatron and partially excluded the aforementioned expected ranges.[31][32][33][34] Based on the data sample collected by the CMS detector at the LHC through the summer of 2011, CMSSM squarks have been excluded up to the mass of 1.1 TeV and gluinos have been excluded up to 500 GeV.[35] Searches are only applicable for a finite set of tested points because simulation using the Monte Carlo method must be made so that limits for that particular model can be calculated. This complicates matters because different experiments have looked at different sets of points. Some extrapolation between points can be made within particular models but it is difficult to set general limits even for the Minimal Supersymmetric Standard Model.

In 2011 and 2012, the LHC discovered a Higgs boson with a mass of about 125 GeV, and with couplings to fermions and bosons which are consistent with the Standard Model. The MSSM predicts that the mass of the lightest Higgs boson should not be much higher than the mass of the Z boson, and, in the absence of fine tuning (with the supersymmetry breaking scale on the order of 1 TeV), should not exceed 130 GeV. Furthermore, for values of the MSSM parameter tan β ≤ 3, it predicts Higgs mass below 114 GeV over most of the parameter space.[36] This region of Higgs mass was excluded by LEP by 2000. The LHC result is somewhat problematic for the minimal supersymmetric model, as the value of 125 GeV is relatively large for the model and can only be achieved with large radiative loop corrections from top squarks, which many theorists consider to be "unnatural" (see naturalness and fine tuning).[37] Furthermore, in 2012, the LHC measured deviations from Standard Model predicted Higgs couplings, particularly in their gamma-gamma final state, which, if they persist, could severely constrain the MSSM.

A summary listed eight arguments against supersymmetry.[38] (1) The LUX experiment for cold dark matter has not observed neutralinos. (2) The large size of the WMAP cold spot is larger than predicted by Lambda cold dark matter models. (3) The large-scale flow of galaxies is larger than predicted by Lambda CDM models. (4) The number of faint dwarf galaxies is smaller than predicted by Lambda CDM models. (5) Neither the ATLAS nor the CMS collaboration have observed gluinos and squarks. (6) The rest mass, interaction cross-section and decay rates of the Higgs boson are compatible with the standard theory, but not with earlier predictions by supersymmetric models. (7) Dirac fermions can be described by a gravitation theory which includes Cartan torsion (Einstein-Cartan theory), supersymmetry is not required. (8) The mass hierarchy problem of Grand Unified theories need not arise if Grand Unification does not exist. The proton decay predicted by Grand Unified theories has not been observed. The quantization of electric charge can be explained by theories which include Dirac magnetic monopoles, so Grand Unification is not necessary.

In spite of the null searches and the heavy Higgs, a recent analysis of the constrained minimal supersymmetric Standard Model, the CMSSM, suggests that the model is still compatible with all present experimental constraints.[39] The preferred masses for squarks and gluinos is about 2 TeV. The resulting fine-tuning of the Higgs boson mass (see little hierarchy problem) and Z-boson mass (see mu problem), however, is considered "unnatural," and some theorists now favor extended supersymmetry models, for example, the NMSSM.

See also

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

Further reading

Supersymmetry and Supergravity page in String Theory Wiki lists more books and reviews.

Theoretical introductions, free and online

Monographs

  • Weak Scale Supersymmetry by Howard Baer and Xerxes Tata, 2006.
  • Cooper, F., A. Khare and U. Sukhatme. "Supersymmetry in Quantum Mechanics." Phys. Rep. 251 (1995) 267-85 (arXiv:hep-th/9405029).
  • Junker, G. Supersymmetric Methods in Quantum and Statistical Physics, Springer-Verlag (1996).
  • Gordon L. Kane.Supersymmetry: Unveiling the Ultimate Laws of Nature Basic Books, New York (2001). ISBN 0-7382-0489-7.
  • Gordon L. Kane and Shifman, M., eds. The Supersymmetric World: The Beginnings of the Theory, World Scientific, Singapore (2000). ISBN 981-02-4522-X.
  • Weinberg, Steven, The Quantum Theory of Fields, Volume 3: Supersymmetry, Cambridge University Press, Cambridge, (1999). ISBN 0-521-66000-9.
  • Wess, Julius, and Jonathan Bagger, Supersymmetry and Supergravity, Princeton University Press, Princeton, (1992). ISBN 0-691-02530-4.
  • Duplij, Steven; Siegel, Warren; Bagger, Jonathan (eds.) (2005). Concise Encyclopedia of Supersymmetry, Springer, Berlin/New York, (Second printing) ISBN 978-1-4020-1338-6

On experiments

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  • Brookhaven National Laboratory (Jan. 8, 2004). New g−2 measurement deviates further from Standard Model. Press Release.
  • Fermi National Accelerator Laboratory (Sept 25, 2006). Fermilab's CDF scientists have discovered the quick-change behavior of the B-sub-s meson. Press Release.

External links

Template:Particles

  1. Sean Carroll, Ph.D., Cal Tech, 2007, The Teaching Company, Dark Matter, Dark Energy: The Dark Side of the Universe, Guidebook Part 2 page 60, Accessed Oct. 7, 2013, "...Supersymmetry -- A hypothetical symmetry relating bosons to fermions..."
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    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  3. http://www.bbc.co.uk/news/science-environment-23431797 BBC
  4. Richard M. Weiner, Spin-statistics-quantum number connection and supersymmetry, Phys. Rev. D 87 (2013) 055003-05, arXiv:1302.0969
  5. 5.0 5.1 5.2 Gordon L. Kane, The Dawn of Physics Beyond the Standard Model, Scientific American, June 2003, page 60 and The frontiers of physics, special edition, Vol 15, #3, page 8 "Indirect evidence for supersymmetry comes from the extrapolation of interactions to high energies." Cite error: Invalid <ref> tag; name "GKane" defined multiple times with different content
  6. Jonathan Feng: Supersymmetric Dark Matter (pdf), University of California, Irvine, 11 May 2007
  7. Torsten Bringmann: The WIMP "Miracle" (pdf) University of Hamburg
  8. http://profmattstrassler.com/articles-and-posts/lhcposts/what-do-current-mid-august-2011-lhc-results-imply-about-supersymmetry/
  9. 9.0 9.1 ATLAS SUSY search documents
  10. 10.0 10.1 CMS SUSY search documents
  11. R. Haag, J. T. Lopuszanski and M. Sohnius, "All Possible Generators Of Supersymmetries Of The S Matrix", Nucl. Phys. B 88 (1975) 257
  12. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  13. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  14. Michio Kaku, Quantum Field Theory, ISBN 0-19-509158-2, pg 663.
  15. Peter Freund, Introduction to Supersymmetry, ISBN 0-521-35675-X, pages 26-27, 138.
  16. Template:Cite doi
  17. D.V. Volkov, V.P. Akulov, Pisma Zh.Eksp.Teor.Fiz. 16 (1972) 621; Phys.Lett. B46 (1973) 109; V.P. Akulov, D.V. Volkov, Teor.Mat.Fiz. 18 (1974) 39
  18. Template:Cite doi
  19. Template:Cite doi
  20. Template:Cite doi
  21. Template:Cite doi
  22. CERN latest data shows no sign of supersymmetry – yet Phys.Org, 25 July 2013
  23. Perimeter Institute and the crisis in modern physics Paul Wells, 5 Sep 2013
  24. Supersymmetry in Disorder and Chaos, Konstantin Efetov, Cambridge university press, 1997.
  25. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  26. Polchinski,J. String theory. Vol. 2: Superstring theory and beyond, Appendix B
  27. LEPSUSYWG, ALEPH, DELPHI, L3 and OPAL experiments, charginos, large m0 LEPSUSYWG/01-03.1
  28. Template:Cite paper
  29. Template:Cite paper
  30. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  31. Implications of Initial LHC Searches for Supersymmetry
  32. Fine-tuning implications for complementary dark matter and LHC SUSY searches
  33. What LHC tells about SUSY
  34. Early SUSY searches at the LHC
  35. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  36. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  37. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  38. "Eight Arguments Against Supersymmetry" http://www.physicsforums.com/showthread.php?t=727664
  39. [1]"Global Fits of the cMSSM and NUHM including the LHC Higgs discovery and new XENON100 constraints", C. Strege, G. Bertone, F. Feroz, M. Fornasa, R. Ruiz de Austri, R. Trotta, arXiv:1212.2636