Time and theSMatrix

A method is introduced for defining the time duration of a scattering process. Using this definition, the connection between causality and analyticity is discussed. An application to three-particle scattering leads to a discussion of the necessity for the existence of stable and unstable particle poles, and finally an analysis is given of rescattering processes and the generation of two-particle normal thresholds, with a view to obtaining Feynman's $i\epsilon$ prescription for deciding which is the physical boundary value.