Microlocal Analysis and Scattering in Quantum Field Theories

Abstract

This chapter focuses on a unified presentation of results on the momentum space analytic structure of the multiparticle S matrix in relativistic quantum theories describing systems of massive particles with short-range interactions, a domain which has been closely linked with purely mathematical developments, for example, in microlocal analysis. The scattering operator S, or S-matrix, relates for each physical system the two free-particle states with which it coincides asymptotically before and after interactions. Non-perturbative theories include a pure S-matrix approach discussed in the chapter, and the axiomatic and constructive theory approaches are also reviewd. The chapter presents some general properties of the S matrix that one aims to establish in field theory approaches in a more precise way. The chapter also reviews the unitarity equations, the macrocausality of S-matrix theory, the pole factorization theorem, local discontinuity formulae, and related results. The nature of singularities and holonomicity properties are discussed in the chapter.