The Gross-Neveu Model under the conditions of violated Lorentz invariance

The aim of this work is to calculate the effective potential in the two-dimensional Gross-Neveu model with violated Lorentz invariance, to study the properties of the obtained potential, and to find extreme points by solving the gap equation and to compare of the results with the theory in the case of nonviolated Lorentz invariance. It is shown that, in the model under study, the effects that make it crucially different from the well-studied model without violation are observed.