Introduction

So far we have limited our attention to four-particle scattering amplitudes (i.e. to processes of the form l + 2 → 3 + 4). These have the advantage of being kinematically rather similar to the potential-scattering amplitudes, for which the basic ideas of Regge theory were originally developed. In particular they depend on only two independent variables, s and t, and so it is a fairly straightforward matter to make analytic continuations in J and t. Also there is a wealth of two-body-final-state data with which to compare the predictions of the theory.

Though the initial state of any physical scattering process will always in practice be a two-particle state (counting bound states such as deuterons as single particles), except at very low energies particle production is always likely to occur. And as the energy increases twobody and quasi-two-body final states make up a diminishing fraction of all the events. So it is very desirable to be able to extend our understanding of Regge theory so as to obtain predictions for many-body final states. Theoretically, this is even more necessary, since models like fig. 3.3 for Regge poles or fig. 8.6 for Regge cuts demonstrate how even in 2 → 2 amplitudes Regge theory makes essential use of manybody unitarity. So if we are to have any hope of making Regge theory self-consistent (in the bootstrap sense, for example) we must be able to describe such intermediate states in terms of Regge singularities.