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Gross-neveu Model




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

:\mathcal{L}=\overline{\psi}_a \left(i\partial\!\!\!/-m ight) \psi^a + rac{g}{2N}\left \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 kind of similar, except that it has Chiral Symmetry .