Some Singularities of Scattering Amplitudes on Unphysical Sheets

Abstract

An investigation of the consequences on unphysical sheets of a Mandelstam-type representation holding for a two-particle scattering amplitude on the physical sheet is described. The domain of analyticity in the energy and momentum transfer variables is constructed and compared with perturbation theory. A theorem on multiplication of singularities for Legendre polynomial expansions used in our discussion is proved.