Gaussian approximation of the Gross-Neveu model in the functional Schrödinger picture

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Abstract
The Gross-Neveu model is analyzed by the Gaussian approximation in the functional Schrödinger picture. It is shown that in the large-N limit the Gaussian approximation exactly reproduces the Gross-Neveu results, but for finite N it contains more information than the large-N approximation. There are two nontrivial phases of the theory depending upon the sign of the infinitesimal bare coupling constant. Dynamical symmetry breaking occurs in one of the phases. We also apply our analysis to the chiral Gross-Neveu model.