General solution of multichannel partial-wave dispersion relations. I

It is shown how to obtain the general solution for the S-matrix of s-wave amplitudes, in the case of n coupled two-body channels whose thresholds coincide. The physical S-matrix is assumed to be the boundary value from above of a function analytic in the whole complex plane with the physical cut and the positions of finite number of simple poles removed. The input consists of the positions of these poles and the residue matrix at each pole. Competing channels are neglected, so that the physical S-matrix is required to be unitary at each energy. Necessary and sufficient conditions are obtained for a solution to exist, and three types of soluble problem are distinguished. To obtain these results the authors have generalized some parts of the Schur-Pick-Nevanlinna interpolation theory to analytic matrices. Some special cases are treated in detail and various results of physical interest pointed out. Particular attention is paid to the characterization of the diagonal components of a solution of a multichannel problem, considered as solutions of inelastic one-channel problems. (Auth.)