This article is primarily devoted to the classical field theory of the sigma model the corresponding quantized theory is presented in the article titled " non-linear sigma model". When the sigma field is coupled to a gauge field, the resulting model is described by Ginzburg–Landau theory. In general, sigma models admit (classical) topological soliton solutions, for example, the Skyrmion for the Skyrme model. An example of the non-quantized version is the Skyrme model it cannot be quantized due to non-linearities of power greater than 4. This manifold can be taken to be any Riemannian manifold, although it is most commonly taken to be either a Lie group or a symmetric space. In physics, a sigma model is a field theory that describes the field as a point particle confined to move on a fixed manifold. Field theory of a point particle confined to move on a fixed manifold
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