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. 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:

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.

References

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