In quantum field theory
are described by anticommuting spinor fields
. A four-fermi 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:
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.