Generalized Retarded Functions and Analytic Function in Momentum Space in Quantum Field Theory

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Abstract
The analytic n‐point function in momentum space in quantum field theory is studied. Its different boundary values for real value of the argument are determined, and a necessary and sufficient condition for them to be obtainable from the Wightman functions is given. The conditions are relativistic covariance, support properties in coordinate space (retardedness), two‐term identities for momentum below threshold (corresponding to spectrum conditions) and four‐term identities (Steinmann relations). The first three conditions are translatable into a statement about the domain of analyticity of the n‐point function: it is analytic in a union of various extended tubes plus the points of contact of two neighboring tubes for real part of one momentum below threshold.