Non-linear sigma model: Difference between revisions

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{{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''' &nbsp;''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.

==Description==

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==External links==

* {{cite journal |doi=10.4249/scholarpedia.8508|title=Nonlinear Sigma model|year=2009|last1=Ketov|first1=Sergei|journal=Scholarpedia|volume=4|issue=1|page=8508|doi-broken-date=2024-06-12 |bibcode=2009SchpJ...4.8508K|doi-access=free}}

* {{cite journal |doi=10.1023/A:1021009008129|year=2002|last1=Kulshreshtha|first1=U.|last2=Kulshreshtha|first2=D. S.|s2cid=115710780|title=Front-Form Hamiltonian, Path Integral, and BRST Formulations of the Nonlinear Sigma Model|journal=International Journal of Theoretical Physics|volume=41|issue=10|pages=1941–1956}}

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[[Category:Quantum field theory]]

[[Category:Mathematical physics]]

[[Category:Murray Gell-Mann]]