Gross-Neveu model

Gross-Neveu model

The Gross-Neveu model is a quantum field theory model of Dirac fermions interacting via four fermion interactions.

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

:mathcal{L}=overline{psi}_a left(ipartial!!!/-m ight) psi^a + frac{g}{2N}left [overline{psi}_a psi^a ight] ^2

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

This model has an U(N) internal symmetry.

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


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