Dispersion Relations and Vertex Properties in Perturbation Theory

Abstract

Dispersion relations for nucleon-nucleon scattering with momentum transfer 2|Δ| ≪ µ, for meson-nucleon scattering, and related properties of the meson-nucleon vertex, are shown to hold in every order perturbation theory. This is done by extending a method used by Nambu to discuss the perturbation-theoretical parametric representations of Green's function. In effect arbitrarily complicated Feynman diagrams are reduced to a few simple types.