Analyticity properties implied by the many-particle structure of then-point function in general quantum field theory

Abstract

This is the first of a series of papers devoted to the derivation of analyticity properties in the non-linear program of general quantum field theory, following the line of the “many particle structure analysis” due to Symanzik. In this preliminary paper, “convolution products” are associated with graphs whose verticesv represent generalnv-point functions. Under convergence assumptions in Euclidean directions, it is proved that any such convolution productHG associated with a graphG withN external lines is well defined as an analytic function of the correspondingN four-momentum variables. The analyticity domain ofHG is proved to contain the correspondingN-point “primitive domain” implied by causality and spectrum and the various real boundary values ofHG satisfy all the relevant linear relations. For appropriate boundary values, the convolution products generalize the perturbative Feynmann prescription. As a by-product of this study, it is proved that in any perturbative theory using “superpropagators” with Euclidean convergence, Feynmann amplitudes that satisfy all the requirements of the linear program can be defined without the help of a regularization.