A Problem of Analytic Completion Related to the Jost-Lehmann-Dyson Formula

Abstract

One considers functions of a complex four-vector Q which are analytic in the domain formed by: (a) The future tube: ImQ in the future light-cone. (b) The past tube: ImQ in the past light-cone. (c) A complex neighborhood of a domain R of real Q space limited by two space-like surfaces. It is shown, by using techniques pertaining to the theory of analytic functions of several complex variables, that all such functions can be analytically continued in a larger domain which coincides with the one predicted by the Jost-Lehmann-Dyson formula.