Absence of mass generation in the d >= 3, N >= 1 weakly coupled Gross-Neveu model - art. no. 107701

We show that the massless (ultraviolet-regularized) Gross-Neveu model, in d greater than or equal to 3 dimensions and any number of flavors (N=1,2,3,. ..), does not exhibit the mass generation mechanism if the quartic term cou pling constant lambda is sufficiently small. Specifically, by showing the u niformity in N for the whole treatment developed for N=1 in previous works, we prove that the two-point function can be written in terms of a converge nt expansion in powers of the initial coupling lambda, with a convergence r adius uniform in N and in the volume, and that, for long distances, it deca ys as a free propagator (i.e., polynomially).