Exact localized solutions of two-dimensional field theories of massive fermions with Fermi interactions

Abstract

The classical equations of motion for field theories of massive fermions with Fermi interactions in one space and one time dimension are investigated. It is shown that they all possess exact stationary solutions which are localized, due to the vanishing of the stress tensor, a feature for this type of solutions only in two dimensions. The explicit forms of these solutions are presented. More importantly, exact solutions for the bound state of $N$ localized massive fermions with scalar or vector Fermi interactions are also found.