Self-ConsistentSMatrix with Regge Asymptotic Behavior

A general discussion is given of the formulation of self-consistent equations for two-body strong-interaction $S$ matrix elements, on the assumption that all poles are of the Regge type and that asymptotic behavior is controlled by these poles. A tentative set of specific equations based on the strip approximation is presented and illustrated by a discussion of the $\pi \pi$ problem. In these equations Regge trajectories and residues for one channel are determined by the top-level Regge poles of the crossed channels. One parameter, the width of the strip, appears in the equations but it is argued that this parameter may be fixed by the principle of maximum strength.