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

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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

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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]}

References

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^ Zee 2010, p. 170.
^ Thies 2014.
^ Kondo 1995.
^ Klevansky 1992.

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Quantum field theories

Theories

Models

Regular	Born–Infeld Euler–Heisenberg Ginzburg–Landau Non-linear sigma Proca Quantum electrodynamics Quantum chromodynamics Quartic interaction Scalar electrodynamics Scalar chromodynamics Soler Yang–Mills Yang–Mills–Higgs Yukawa
Low dimensional	2D Yang–Mills Bullough–Dodd Gross–Neveu Schwinger Sine-Gordon Thirring Thirring–Wess Toda
Conformal	2D free massless scalar Liouville Logarithmic Minimal Polyakov Wess–Zumino–Witten
Supersymmetric	4D N = 1 N = 1 super Yang–Mills Seiberg–Witten Super QCD Wess–Zumino
Superconformal	6D (2,0) ABJM N = 4 super Yang–Mills
Supergravity	Pure 4D N = 1 4D N = 1 4D N = 8 Higher dimensional Type I Type IIA Type IIB 11D
Topological	BF Chern–Simons
Particle theory	Chiral Fermi MSSM Nambu–Jona-Lasinio NMSSM Standard Model Stueckelberg

See also:

Template:Quantum mechanics topics

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Four-fermion interactions

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Relativistic models

Nonrelativistic models

See also

References

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Four-fermion interactions

Relativistic models

Nonrelativistic models

See also

References

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