Gross-Neveu model

We have N Dirac fermions, ψ₁, ..., ψ_N. The Lagrangian density is

$\mathcal{L}=\overline{\psi}_a \left(i\partial\!\!\!/-m \right) \psi^a + \frac{g}{2N}\left[\overline{\psi}_a \psi^a\right]^2$

using the Einstein summation notation where g is the coupling constant. If the mass m is nonzero, the model is massive.

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See also Nambu-Jona-Lasinio model which is similar, except that it has chiral symmetry.

Four-fermion interactions
Fermi's theory Thirring model Gross-Neveu model Nambu-Jona-Lasinio model BCS theory Hubbard model Luttinger liquid