Macroscopic causality and physical region analyticity in S-matrix theory

Abstract

An equivalence is proved between a certain macroscopic causality condition and the normal analytic structure of the physical-regionS-matrix. The normal analytic structure is this: each scattering function has physical-region singularities only on positive-α Landau surfaces and near these surfaces it is the limit from certain well-defined directions of a unique analytic function. The macroscopic causality condition is formulated in terms ofS-matrix concepts. It expresses the requirement that in an appropriate classical macroscopic limit all transition amplitudes fall off in the way indicated by classical estimates. This result gives, on the one hand, a physical basis for the basic physical-region analyticity properties of theS matrix. On the other hand, it gives, alternatively, a basis for a space-time description of phenomena starting from momentum space properties having noa priori space-time content.