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In quantum field theory, a nonlinear σ model describes a scalar field Σ which takes on values in a nonlinear manifold called the target manifold T. The non-linear σ-model was introduced by Gell-Mann & Lévy (1960, section 6), who named it after a field corresponding to a spinless 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.

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