Semiclassical bound states in an asymptotically free theory

Abstract

We have carried out a semiclassical calculation of the particle spectrum in the Gross-Neveu model. It is a two-dimensional model with $N$ species of fermions interacting through a symmetrical scalar-scalar interaction and is renormalizable, asymptotically free, and exhibits spontaneous symmetry breaking. We find a rich spectrum of particles which can be interpreted as fermion-antifermion bound states and multifermion bound states. These states fall into supermultiplets whose origin we do not completely understand. The binding mechanism is a vacuum-polarization effect rather than the direct interaction between particles. A general method for handling fermions in semiclassical calculations is developed.