Spectral Representations in Perturbation Theory. II. Two-Particle Scattering

In this paper a particular term in the perturbation expansion for the two-particle scattering amplitude is examined. We consider the real plane defined by the square of the total four-momentum and the square of the momentum transfer, and show that the scattering amplitude is an analytic function of both variables in a certain connected region in this plane. The precise boundary of the region is found. The purpose of this work is to find some conditions that integral representations of the scattering amplitude must satisfy, with the hope that such examples may aid the study of such integral representations in general.We also apply our general result to some particular cases of physical interest.