Misplaced Pages

This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Four-fermion interactions" – news · newspapers · books · scholar · JSTOR (December 2009) (Learn how and when to remove this message)

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. Local here means that it all happens at the same spacetime point. This might be an effective field theory or it might be fundamental.

Relativistic models

Some examples are the following:

• Fermi's theory of the weak interaction. The interaction term has a V − A (vector minus axial) form.
• The Gross–Neveu model. 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. This is a four-fermi theory of fermions with a vector coupling.
• The Nambu–Jona-Lasinio model. This is a four-fermi theory of Dirac fermions with chiral symmetry and as such, it has no bare mass.

Nonrelativistic models

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.

In four space-time dimensions, such theories are not renormalisable.

See also

• Oblique correction

• Peskin–Takeuchi parameter

v t e Quantum field theories
Theories	Algebraic QFT Axiomatic QFT Conformal field theory Lattice field theory Noncommutative QFT Gauge theory QFT in curved spacetime String theory Supergravity Thermal QFT Topological QFT Two-dimensional conformal field theory
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 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
Related	Casimir effect Cosmic string History Loop quantum gravity Loop quantum cosmology On shell and off shell Quantum chaos Quantum dynamics Quantum foam Quantum fluctuations links Quantum gravity links Quantum hadrodynamics Quantum hydrodynamics Quantum information Quantum information science links Quantum logic Quantum thermodynamics
See also: Template:Quantum mechanics topics

This quantum mechanics-related article is a stub. You can help Misplaced Pages by expanding it.

• v
• t
• e

• Quantum field theory
• Quantum physics stubs