THE GENERALIZED HARTREE-FOCK METHOD IN THE GROSS-NEVEU MODEL

In the generalized Hartree-Fock scheme one can incorporate nonperturbative effects from the beginning of a diagrammatic expansion. In order to make a detailed analysis of the method, we apply it to the Gross-Neveu model as an example and calculate the chiral condensate at large N by using a direct diagrammatic expansion. The unperturbed Gaussian kernel is adjusted to be massive by adding fermion mass terms and the mass terms are subtracted from the interaction part, thus not changing the full Lagrangian. The chiral condensate (g sigma) is expanded in powers of the renormalized coupling constant and then improved by the method of effective charges. We find that our diagrammatic expansion is compatible with renormalisation. By using the principle of minimal sensitivity, we evaluate (g sigma) and show that the exact broken and unbroken solutions for the discrete gamma(5) symmetry are obtained at each order of the expansion.