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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. Local here means that it all happens at the same spacetime point. This might be an effective field theory or it might be fundamental.
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.
In four space-time dimensions, such theories are not renormalisable.
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