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Non-linear sigma model

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In quantum field theory, a nonlinear σ model describes a field Σ that takes on values in a nonlinear manifold called the target manifold  T. The non-linear σ-model was introduced by Gell-Mann & Lévy (1960, §6), who named it after a field corresponding to a sp meson called σ in their model. This article deals primarily with the quantization of the non-linear sigma model; please refer to the base article on the sigma model for general definitions and classical (non-quantum) formulations and results.