|
|
| Line 1: |
Line 1: |
| In [[physics]], a '''sigma model''' is a [[physical system]] that is described by a [[Lagrangian density]] of the form:
| | Hi there. Allow me begin psychic solutions by lynne ([http://brazil.amor-amore.com/irboothe http://brazil.amor-amore.com/irboothe]) introducing the author, her title is Sophia. To perform domino is some thing I really enjoy performing. Alaska is where I've always been residing. My day occupation is an info officer but I've currently utilized for an additional one. |
| | |
| :<math>\mathcal{L}(\phi_1, \phi_2, \ldots, \phi_n) = \sum_{i=1}^n \sum_{j=1}^n g_{ij} \; \mathrm{d}\phi_i \wedge {*\mathrm{d}\phi_j}</math>
| |
| | |
| Depending on the scalars in {{math|''g''<sub>''ij''</sub>}}, it is either a linear sigma model or a [[non-linear sigma model]]. The fields {{math|φ<sub>i</sub>}}, in general, provide a [[map]] from a base manifold called the [[worldsheet]] to a target (Riemannian) manifold of the scalars linked together by internal symmetries. (In string theory, however, that is often understood to be the actual [[spacetime]].)
| |
| | |
| The sigma model was introduced by {{harvtxt|Gell-Mann|Lévy|1960|loc=section 5}}; the name '''σ-model''' comes from a field in their model corresponding to a spinless meson called {{mvar|σ}}, a scalar introduced earlier by Schwinger. The model served as the dominant prototype of [[spontaneous symmetry breaking]] of O(4) down to O(3): the three axial generators broken are the simplest manifestation of [[chiral symmetry breaking]], the surviving unbroken O(3) representing isospin.
| |
| | |
| A basic example is provided by [[quantum mechanics]] which is a [[quantum field theory]] in one dimension. It's a sigma model with a base manifold given by the real line parameterizing the time (or an interval, or the circle, etc.) and a target space that is the real line.
| |
| | |
| The model may be augmented by a [[torsion tensor|torsion]] term to yield the more interesting [[Wess–Zumino–Witten model]].
| |
| | |
| ==References==
| |
| | |
| *{{Citation
| |
| | last1=Gell-Mann | first1=M.
| |
| | last2=Lévy | first2=M.
| |
| | year=1960
| |
| | title=The axial vector current in beta decay
| |
| | journal=[[Il Nuovo Cimento]]
| |
| | volume=16 | pages=705–726
| |
| | doi=10.1007/BF02859738
| |
| }}
| |
| | |
| | |
| [[Category:Quantum field theory]]
| |
| [[Category:Physical systems]]
| |
Hi there. Allow me begin psychic solutions by lynne (http://brazil.amor-amore.com/irboothe) introducing the author, her title is Sophia. To perform domino is some thing I really enjoy performing. Alaska is where I've always been residing. My day occupation is an info officer but I've currently utilized for an additional one.