Question

Whats the difference between a linear and non-linear sigma model?

Answer 1

Question: what exactly are the conditions on that distinguish a linear sigma model from a non-linear one?
The article further adds:
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.
This suggests that the sigma model is in fact a section of a principal bundle with a structure group that represents the internal symmetries.

Answer 2

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✔In quantum field theory, a nonlinear σ modeldescribes a scalar field  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.

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