Single-Particle Green's Function for a One-Dimensional Many-Fermion System

In this paper we compute the single-particle Green's function for a system of N-interacting fermions in one dimension. The problem is exactly soluble in the case of a δ-function potential. We consider also the case of a small modification to a δ-function potential and we compute the Green's function up to first order in a perturbation expansion. In both cases we find that the Green's function has a branch cut in the complex energy plane but it has no single-particle poles.