{{Short description|Class of quantum field theory models}}
In [[quantum field theory]], a '''nonlinear ''σ'' model''' describes a [[scalar field]] {{mvar|Σ}} whichthat takes on values in a nonlinear manifold called the '''target manifold''' ''T''. The non-linear ''σ''-model was introduced by {{harvtxt|Gell-Mann|Lévy|1960|loc=section §6}}, who named it after a field corresponding to a spinless[[spin (physics)|sp]] [[meson]] called ''σ'' in their model.<ref>{{Citation | last2=Lévy | first1=M. | last1=Gell-Mann | first2=M. | s2cid=122945049 | title=The axial vector current in beta decay | publisher=Italian Physical Society | doi=10.1007/BF02859738 | year=1960 | journal=Il Nuovo Cimento | issn=1827-6121 | volume=16 | issue=4 | pages=705–726| bibcode=1960NCim...16..705G }}</ref> 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.
