Macrocausality, Unitarity and Discontinuity Formulae in $S$-Matrix Theory

Abstract

The purpose of this lecture is to present general physical-region properties of multiparticle scattering amplitudes in relativistic quantum theory. The emphasis will be on recent developments. S-matrix theory has been mainly developed for systems of massive particles with shortrange interactions (i.e. strong interactions) and we only consider here this case. The key notion which has appeared to be of basic importance, at begining of sixties, in study of collision amplitudes is that of analyticity. In this lecture, I am concerned only with momentum-space analyticity properties in physical region. (The physical region of a process is real mass-shell region associated with this process. Precise definitions will be recalled later). Besides its own interest, knowledge of physical region structure of multiparticle amplitudes will give precise indications on general analyticity properties which can be expected away from physical region, on complex mass-shell, as explained in lectures by Professor Stapp. Historically, derivation of analyticity properties has been based in first part of sixties on idea that the scattering functions should have maximal analyticity consistent with unitarity. With regard to physical-region, program is then to determine analytic structure of S-matric from unitarity and a certain ze postulate. Although this approach still keeps its own interest, it has not been possible so far to establish S-matrix theory on firm and precise bases in this