Bound states and solitons in the Gross--Neuveu model

The results for the spectrum of bound states and of solitons first deduced by Dashen, Hasslacher, and Neveu for a model of interacting fermions by techniques of functional integration are obtained here by methods based on Heisenberg field mechanics analogous to those applied previously to models of self interacting bosons. The method of solution is suggested by a simplified physical picture of the bound states: These are computed in a Hartree approximation in which the self-consistent potential is a sum of contributions from the fermions (and antifermions) occupying orbitals in the conventional many-body picture and from the vacuum fluctuations of single closed loop type. In the same approximation the self-consistent field generated by the heavy soliton is a creature of the vacuum fluctuations alone. As the main new technical contribution, equations determining the self-consistent fields as well as the amplitudes (''wave-functions'') from which these are constructed are deduced and solved. Comment is given on the degeneracy of the heavy soliton state