Time dependence of elementary processes

Abstract

There is a number of inequivalent descriptions of time-dependent processes, which give approximately the same time dependence in standard cases. However, substantial differences occur for other situations. Also, looking for finer details makes only sense if one has an adequate description. Moreover, unique prescriptions are of importance for the study of weak interactions. We therefore analyze typical experimental situations and their connection with quantum theoretic probabilities. The most important cases are considered in detail. If stable, possibly composite particles are observed initially and finally, everything can be based on the exact formulation of multichannel scattering theory. If unstable particles are actually detected, suitable Hilbert space vectors have to be defined. Various properties of the resulting probabilities are pointed out. Usual approaches are critically discussed.