Analytic Properties of Products of Field Operators

Abstract

It is shown that any function of n−1 four-vectors which is analytic in the forward tube, the backward tube, and some neighborhood of the Jost points has a one-valued continuation into the extended tube. The theorem is applied to products of field operators between arbitrary states. It is shown that each matrix element of the product is analytic in the envelope of holomorphy of the union of the permuted extended tubes (the domain of analyticity of the most general causal vacuum expectation value). Thus the product of field operators may be regarded as having analytic properties.