Multi-channel Bethe-Salpeter equation

A general form of multi-channel Bethe-Salpeter equation is considered. In c ontradistinction to the hitherto applied approaches, our coupled system of equations leads to the simultaneous solutions for all relativistic four-poi nt Green functions (elastic and inelastic) appearing in a given theory. A s et of relations which may be helpful in approximate treatments is given. An example of extracting useful information from the equations is discussed: we consider the most general trilinear coupling of N different scalar field s and obtain - in the ladder approximation - closed expressions for the Reg ge trajectories and their couplings to different channels in the vicinity o f l = -1. Sum rules and an example containing non-obvious symmetry are disc ussed.