Absence of Mass Generation in the d 3 , N 1 Weakly CoupledGross - Neveu

We show that the massless (ultraviolet regularized) Gross-Neveu model, in d 3 dimensions and any number of avors (N = 1; 2; 3; : : :), does not exhibit the mass generation mechanism if the quartic term coupling constant is suuciently small. In particular, extending previous results (rigorously established for N = 1 1,2]) we prove that the two-point function can be written in terms of a convergent expansion in powers of the initial coupling , with a convergence radius independent on N and uniform in the volume, and that its long distance decay is polynomial, such as the free propagator behavior. In this paper, we shall consider the following Euclidean version for the Gross-Neveu (GN) action (later, we still introduce an ultraviolet cutoo)