Variational Solution of the Gross-Neveu Model: finite $N$ and Renormalization

Abstract

We show how to perform systematically improvable variational calculations in the $O(2N)$ Gross-Neveu model for generic $N$, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the perturbative renormalization group . The final point is a general framework for the calculation of non-perturbative quantities like condensates, masses etc$\dots$, in an asymptotically free field theory. For the Gross-Neveu model, the numerical results obtained from a ``2-loop'' down to low values of $N$.

35 pages, Latex, 5 figures. Correction of a trivial mistake in the Padé approximant numerical program leads to a significant improvement of the variational results for the mass gap, for arbitrary N. A more complete comparison of different Padé approximants is performed. Text modified according to these new results, one figure and two references added