Regge Pole Theory and Unitarity

Abstract

Under the assumptions that are the case for non-relativistic theory, it is shown that the Regge pole theory is compatible with unitarity only if the Regge singularities are infinite in number. If we merely take account of a finite number of them, unitarity is justified in restricted regions such as t~oo and s~s0 • We also show that the double spectral function on which unitarity imposes some restrictions can be constructed by the use of an infinite set of the parallel daughter trajectories. Therefore introduction of these trajectories can remove the difficulties between the Regge pole theory and unitarity.