Dispersion relations for analytically continued partial-wave amplitudes in potential theory

Abstract

The dispersion relations of Fivel are extended to physically meaningful situations. On the basis of the Mandelstam representation and a modified form of the partial-wave expansion a closed system of equations is obtained for the partial-wave amplitude for values of the angular momentum defined by reall equal to a constant positive number. A solution by iteration is indicated. The assumption is made that the partial-wave amplitude has a rightmost singularity in the complex angular momentum plane. The methods of the paper are extended to provide a new derivation of the integral equation satisfied by the Mandelstam spectral function.