Rg Generated Fermion Mass

Chiral symmetry breaking in a purely fermionic theory is investigated by the help of the renormalization group method. The RG equation for the running mass m k admits a solution with vanishing bare mass and finite physical mass. The running Fermi coupling constant, G k , converges to a finite (renormalized) physical value. It is also shown that the RG equation for˜G, the dimensionless Fermi coupling, has an UV fixed point˜G U V. Contrary to a previous result however, it is proven that the chiral symmetry breaking point˜G c does not coincide with˜G U V. The problem of the dynamical generation of a fermion mass has been studied over the years by several authors[1]. Nambu and Jona-Lasinio (NJL) considered a purely fermionic model in the mean field approximation and found a non trivial solution for the fermion mass, for values of the Fermi constant larger than a critical one [2]. The non perturbative nature of this approximation is obvious as the chiral symmetry of the model forbids the appearance of a mass term at any order of perturbation theory. Here I study a fermionic model by the help of a different non-perturbative technique, the renormalization group method. It is widely recognized that the approach pioneered by Wilson[3] provides a powerful method to study quantum and statistical field theories. In the Wegner-Houghton[4] realization it is implemented by establishing an exact integro-differential flow equation