Generalization of the Gross–Neveu model to the case of several coupling constants

The two-dimensional massless four-fermion theory (1) with several coupling constants is considered in the $1/N$ approximation. This model is asymptotically free. For all values of the coupling constants, there is dynamical breaking of the chiral invariance in it, and the fermions acquire masses. It is shown that there exist two different phases with massive fermions. Necessary and sufficient conditions under which the theory does not have ghosts are found. In the leading order in $1/N$, the model contains bosons with two different masses.