Time delay in <i>N</i>-body scattering

Abstract

We extend the theory of time delay to N-body scattering. The known results relating time delay to the S matrix in the two-body and three-body problem suggest that these relationships are universal. Within the context of two-Hilbert space N-body scattering theory an abstract definition of time delay is provided. For all scattering processes initiated by the collision of two clusters a simple proof is constructed establishing the connection of time delay to the on-shell S matrix and its energy derivatives. The definition of time delay and method of proof given here are compared with earlier approaches used in the three-body problem.