Main Page: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
No edit summary
No edit summary
 
(442 intermediate revisions by more than 100 users not shown)
Line 1: Line 1:
{{Unreferenced|date=December 2009}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
In [[physics]], an '''infrared fixed point''' is a set of coupling constants, or other parameters that evolve from initial values at very high energies (short distance), to fixed stable values, usually predictable, at low energies (large distance). This usually involves the use of the [[renormalization group]], a mathematical apparatus for theoretically evolving physical systems from one scale to another.


Conversely, if the length-scale decreases and the physical parameters approach fixed values, then we have [[ultraviolet fixed point]]s. The fixed points are generally independent of the initial values of the parameters over a large range of the initial values. This is known as "[[Background independence|universality]]".
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


==Statistical physics==
Registered users will be able to choose between the following three rendering modes:
In the [[statistical physics]] of second order [[phase transition]]s, the physical system approaches an infrared fixed point that is independent of the
initial short distance dynamics that defines the material. This determines the properties of the phase transition at the [[critical temperature]], or  [[critical point (thermodynamics)|critical point]]. Observables, such as "[[critical exponents]]" usually depend only upon dimension of space, and are independent of the atomic or molecular constituents.


==Particle physics==
'''MathML'''
In particle physics the best known fixed point is that the [[strong interaction]]'s [[coupling constant]] gets closer to zero as the energy increases. This is an ultraviolet fixed point, associated with the phenomenon known as '[[asymptotic freedom]]'. This causes [[quark]]s and [[gluon]]s to behave as effectively [[free particle|free]] noninteracting particles at high energies. This phenomenon was first anticipated by "[[Bjorken Scaling]]", and observed in electroproduction experiments. It was critical to the development of [[quantum chromodynamics]].
:<math forcemathmode="mathml">E=mc^2</math>


There is a remarkable infrared fixed point of the coupling constants that determine the masses of very heavy quarks. In the [[Standard Model]], quarks and leptons have "[[Yukawa coupling]]s" to the [[Higgs boson]]. These determine the mass of the particle. All of the quarks' and leptons' Yukawa couplings are small compared to the [[top quark]]'s Yukawa coupling. Yukawa couplings are not constants and their properties change depending on the energy scale at which they are measured, this is known as ''[[running]]'' of the constants. The dynamics of Yukawa couplings are determined by the [[Exact renormalization group equation|renormalization group equation]]:
<!--'''PNG''' (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


<math>\mu \frac{\partial}{\partial\mu} y  \approx \frac{y}{16\pi^2}\left(\frac{9}{2}y^2 - 8 g_3^2\right)</math>,
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


where <math>g_3</math> is the [[color charge|color]] [[gauge theory|gauge]] coupling (which is a function of  <math>\mu</math> and associated with [[asymptotic freedom]])  and <math>y</math> is the Yukawa coupling. This equation describes how the Yukawa coupling changes with energy scale <math>\mu</math>.
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


The Yukawa couplings of the up, down, charm, strange and bottom quarks, are small at the extremely high energy scale of [[Grand Unified Theory|grand unification]], <math> \mu \approx 10^{15} </math> GeV.  The <math>y^2</math> term can be neglected in the above equation. Solving, we then find that <math>y</math>  is increased slightly at the low energy scales at which the quark masses are generated by the Higgs, <math> \mu \approx 100 </math> GeV.
==Demos==


On the other hand, solutions to this equation for large initial values <math>y</math> cause the ''rhs'' to quickly approach zero. This locks <math>y</math> to the QCD coupling <math>g_3</math>. This is known as a (quasi-infrared) fixed point of the renormalization group equation for the Yukawa coupling.  No matter what the initial starting value of the coupling is, if it is sufficiently large it will reach this fixed point value, and the corresponding quark mass is predicted.
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


The value of the fixed point is fairly precisely determined in the Standard Model, leading to a predicted top quark mass of 230 &nbsp;GeV. If there is more than one Higgs doublet, the value will be reduced by Higgs [[mixing angle]] effects.  The observed top quark mass is slightly lower, about 171 GeV (see [[top quark]]).


In the minimal supersymmetric extension of the Standard Model ([[Minimal Supersymmetric Standard Model|MSSM]]), there are two Higgs doublets and the renormalization group equation for the top quark Yukawa coupling is slightly modified. This leads to a fixed point where the top mass is smaller, 170–200&nbsp;GeV. Some theorists believe this is supporting evidence for the MSSM.
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


The  "quasi-infrared fixed point" was proposed in 1981 by [[C. T. Hill]], B. Pendleton and G. G. Ross. The prevailing view at the time was that the top quark mass would lie in a range of 15 to 26 GeV. The quasi-infrared fixed point has formed the basis of [[top quark condensation]] theories of electroweak symmetry breaking in which the Higgs boson is composite at ''extremely'' short distance scales, composed of a pair of top and anti-top quarks. Many authors have explored other aspects of infrared fixed points to understand the anticipated spectrum of Higgs bosons in multi-Higgs models.
==Test pages ==


Another example of an infrared fixed point is the [[Banks-Zaks fixed point]] in which the coupling constant of a Yang-Mills theory evolves to a fixed large value. The beta-function vanishes, and the theory possesses a symmetry known as [[conformal symmetry]].
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


==See also==
*[[Inputtypes|Inputtypes (private Wikis only)]]
* [[Top quark]]
*[[Url2Image|Url2Image (private Wikis only)]]
* [[Cutoff (physics)]]
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
{{DEFAULTSORT:Infrared Fixed Point}}
[[Category:Quantum field theory]]
[[Category:Statistical mechanics]]
[[Category:Conformal field theory]]
[[Category:Renormalization group]]
[[Category:Fixed points (mathematics)]]
 
[[es:Punto fijo infrarrojo]]

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

Retrieved from "https://en.formulasearchengine.com/index.php?title=Main_Page&oldid=329754"