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

TL;DR

This paper develops a systematic variational approach for the Gross-Neveu model at finite N, effectively handling infinities and enabling non-perturbative calculations like condensates and masses in an asymptotically free theory.

Contribution

It introduces a general framework for variational calculations that incorporate renormalization, applicable to non-perturbative quantities in the Gross-Neveu model at any N.

Findings

Numerical results from 2-loop calculations at low N.

Framework effectively manages infinities in variational methods.

Applicable to non-perturbative quantities in asymptotically free theories.

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$\ldots$, in an asymptotically free field theory. For the Gross-Neveu model, the numerical results obtained from a ``2-loop'' down to low values of $N$.