Massive Gross-Neveu Model: A Rigorous Perturbative Construction

Abstract

We consider the massive Euclidean Gross-Neveu model. Thanks to the Pauli principle the bare perturbation expansion for the model with an ultraviolet cutoff is convergent in a disk whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant. The theory constructed in this way is physical (it satisfies Osterwalder and Schrader's axioms) in contrast with the planar theories obtained by similar perturbative expansions.