Generalized Gross-Neveu model in d dimensions. Cross-over and fermion masses

摘要

By considering a non-trivial extension of previous techniques, the wilsonian renormalization group equation for a generalized. N flavors Gross-Neveu model in. d≥2 dimensions is established. This equation is then tested by computing the critical exponents and the anomalous dimension of composite operators for. d<4 at the leading order of the large. N expansion and the results are found to be in agreement with those obtained (at the same order) with more conventional approaches based on bosonization. This is the first time that for dimensions. d close to. d=4 these quantities are computed by referring directly to the fermion degrees of freedom of the model, i.e., with no reference to its bosonized version. With the help of our equations, we then propose a dynamical mechanism for the generation of fermion masses that results from a cross-over phenomenon. Such a mechanism could be relevant, in particular, for models which do not include fundamental scalars. Moreover, we find that the celebrated NJL result is recovered as an approximate solution to our equations. This seems to suggest that the physical origin of the NJL mechanism could be routed in the cross-over transition discussed in the present work.