Four-fermion interactions
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In quantum field theory, fermions are described by anticommuting spinor fields. A four-fermion interaction describes a local interaction between four fermionic fields at a point in spacetime. A theory involving such an interaction might be an effective field theory or it might be fundamental.
In four spacetime dimensions, such theories are not renormalisable.[citation needed]
Relativistic models
[edit]Some examples are the following:
- Fermi's theory of the weak interaction.[1] The interaction term has a V − A (vector minus axial) form.
- The Gross–Neveu model.[2] This is a four-fermi theory of Dirac fermions without chiral symmetry and as such, it may or may not be massive.
- The Thirring model.[3] This is a four-fermi theory of fermions with a vector coupling.
- The Nambu–Jona-Lasinio model.[4] This is a four-fermi theory of Dirac fermions with chiral symmetry and as such, it has no bare mass.
Nonrelativistic models
[edit]A nonrelativistic example is the BCS theory at large length scales with the phonons integrated out so that the force between two dressed electrons is approximated by a contact term.[citation needed]
See also
[edit]References
[edit]- ^ Zee 2010, p. 170.
- ^ Thies 2014.
- ^ Kondo 1995.
- ^ Klevansky 1992.
- Klevansky, S. P. (1992). "The Nambu—Jona-Lasinio model of quantum chromodynamics". Reviews of Modern Physics. 64 (3): 649–708. doi:10.1103/revmodphys.64.649.
- Kondo, Kei-ichi (1995). "Thirring model as a gauge theory". Nuclear Physics B. 450 (1–2): 251–266. arXiv:hep-th/9502070. doi:10.1016/0550-3213(95)00316-K.
- Thies, Michael (2014). "Integrable Gross-Neveu models with fermion-fermion and fermion-antifermion pairing". Physical Review D. 90 (10): 105017. arXiv:1408.5506. doi:10.1103/PhysRevD.90.105017.
- Zee, Anthony (2010). Quantum Field Theory in a Nutshell (2nd ed.). Princeton University Press. ISBN 9780691140346.