Power Series Expansion for a Crossing-Symmetric Vertex Function

摘要

Starting from a nonlinear system of coupled integral equations for the vertex parts which are irreducible with respect to the s, t and u channel, a power series is found for the full vertex function in terms of the vertex part gamma (0) which is irreducible with respect to all channels. The problem of finding an expression in closed form remains unresolved, since higher order products in gamma (0) are nonassociative. In a simplified model, the mathematical properties of the series seem to allow successive rational approximations. Specific reference is made to the Green's function formulation of the many body theory.