Four-fermion interactions

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

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

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

• Oblique correction
• Peskin–Takeuchi parameter