Gaussian approximation of the (2 + 1)-dimensional Gross-Neveu model

Abstract

The (2 + 1)-dimensional Gross-Neveu model is analyzed by the Gaussian approximation in the functional Schr\"odinger picture. It is shown that the Gaussian effective potential implies the existence of two phases, and one of them is inconsistent. In the phase where the bare coupling constant approaches positive infinitesimal, the effective potential shows the existence of dynamical symmetry breaking when the renormalized coupling constant is negative.