Gross-Neveu model

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

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.

This model has an U(N) internal symmetry.

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

v • d • e Four-fermion interactions

Fermi's interaction • Thirring model • Gross-Neveu model • Nambu-Jona-Lasinio model BCS theory • Hubbard model • Luttinger liquid

v • d • e Quantum field theories

Standard	Chern-Simons model · Chiral model · Kondo model · Lower dimensional quantum field theory · Minimal model · Noncommutative quantum field theory · Non-linear sigma model · Phi to the fourth · Quantum chromodynamics · Quantum electrodynamics · Quantum Yang-Mills theory · Schwinger model · Sine-Gordon · Standard Model · String Theory · Toda field theory · Topological quantum field theory · Wess-Zumino model · Wess-Zumino-Witten model · Yang–Mills · Yang–Mills–Higgs model · Yukawa model

Four-fermion interactions	Thirring model · Gross-Neveu · Nambu-Jona-Lasinio