The evaluation of Feynman integrals in the physical region using multi-valued approximants

Abstract

An extension of the computational technique of Chisolm, Genz, and Putersla (1976) for evaluating Feynman matrix elements in the physical region is presented. The extension is based upon the use of certain multi-valued approximants as a summation method for divergent series; these approximants replace the Pade approximants used previously. The use of these multi-valued approximants enables the singularity structure of Feynman integrals on unphysical sheets to be investigated numerically, and we show that the approximants provide a practical method for the analytic continuation of a function from one Riemann sheet to another. The author also discusses this technique in relation to two-variable approximants and investigate the multi-valued approximants recently defined by Chisholm (1978).