Microcausality, macrocausality and the physical region (micro)analytic S-matrix

Recent works on the physical region analytic structure of multiparticle collision amplitudes in relativistic quantum theory are presented. First, the structure that can be expected and which is the expression, in terms of general essential support or microanalyticity properties, of macrocausality and macrocausal factorization, is described. It is shown that, taken together, these properties are equivalent to decompositions of the S-matrix, in bounded parts of the physical region, in terms of generalized Feynman integrals. Derivations of this structure obtained recently for 3 → 3 processes below the four-particle threshold both in S-matrix theory (without recourse to the crucial ad hoc assumption of 'separation of singularities' in unitarity equations used previously) and in axiomatic field theory are then reviewed. It is finally explained how this structure applies in two-dimensional space-time and yields factorization of the multiparticle S-matrix itself for a class of models. (orig.)