Sigma model
In physics, a sigma model is a physical system that is described by a Lagrangian density of the form:
Depending on the scalars in, it is either a linear sigma model or a non-linear sigma model. The fields, 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.Overview
The sigma model was introduced by ; the name σ-model comes from a field in their model corresponding to a spinless meson called, a scalar meson introduced earlier by Julian Schwinger. The model served as the dominant prototype of spontaneous symmetry breaking of O down to O: the three axial generators broken are the simplest manifestation of chiral symmetry breaking, the surviving unbroken O 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 and a target space that is the real line.
The model may be augmented by a torsion term to yield the Wess–Zumino–Witten model.
