Chiral model

In nuclear physics, the chiral model, introduced by Feza Gürsey in 1960, is a phenomenological model describing effective interactions of mesons in the chiral limit (where the masses of the quarks go to zero), but without necessarily mentioning quarks at all. It is a nonlinear sigma model with the principal homogeneous space of the Lie group SU(N) as its target manifold, where N is the number of quark flavors. The Riemannian metric of the target manifold is given by a positive constant multiplied by the Killing form acting upon the Maurer-Cartan form of SU(N).

The internal global symmetry of this model is SU(N)_L×SU(N)_R, the left and right copies, respectively; where the left copy acts as the left action upon the target space, and the right copy acts as the right action. The left copy represents flavor rotations among the left-handed quarks, while the right copy describes rotations among the right-handed quarks, while these, L and R, are completely independent of each other. The axial pieces of these symmetries are spontaneously broken so that the corresponding scalar fields are the requisite Nambu−Goldstone bosons.

This model admits topological solitons called Skyrmions.

References

Gürsey, F. (1960). "On the symmetries of strong and weak interactions". Il Nuovo Cimento 16 (2): 230–240. doi:10.1007/BF02860276.
Coleman, S.; Wess, J.; Zumino, B. (1969). "Structure of Phenomenological Lagrangians. I". Physical Review 177 (5): 2239. Bibcode:1969PhRv..177.2239C. doi:10.1103/PhysRev.177.2239. ; Callan, C.; Coleman, S.; Wess, J.; Zumino, B. (1969). "Structure of Phenomenological Lagrangians. II". Physical Review 177 (5): 2247. Bibcode:1969PhRv..177.2247C. doi:10.1103/PhysRev.177.2247.
Bulgac, Aurel; Miller, Gerald; Strikman, Mark (1997). "Chiral limit of nuclear physics". Physical Review C 56 (6): 3307. arXiv:nucl-th/9708045. Bibcode:1997PhRvC..56.3307B. doi:10.1103/PhysRevC.56.3307.
Meißner, Ulf-G. (2005). "The chiral limit of QCD and above". Nuclear Physics A 755: 161. arXiv:hep-ph/0501009. Bibcode:2005NuPhA.755..161M. doi:10.1016/j.nuclphysa.2005.03.139.
Chang-Fang, Lu; Xiao-Fu, Lü (2010). "Mixed Quark-Gluon Condensate Beyond Chiral Limit". Communications in Theoretical Physics 53 (5): 893. Bibcode:2010CoTPh..53..893L. doi:10.1088/0253-6102/53/5/19.
Fry, M. P. (2000). "Chiral limit of the two-dimensional fermionic determinant in a general magnetic field". Journal of Mathematical Physics 41 (4): 1691. arXiv:hep-th/9911131. Bibcode:2000JMP....41.1691F. doi:10.1063/1.533204.

Quantum field theories

Standard	Chern–Simons model Chiral model Kondo model Conformal field theory Noncommutative quantum field theory Non-linear sigma model Quartic interaction Quantum chromodynamics Quantum electrodynamics Quantum Yang–Mills theory Schwinger model sine-Gordon Standard Model String theory Toda field theory Topological quantum field theory Wess–Zumino model Wess–Zumino–Witten model Yang–Mills theory Yang–Mills–Higgs model Yukawa model Thirring–Wess model

Four-fermion interactions	Thirring model Gross–Neveu model Nambu–Jona-Lasinio model

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