The most general solution to the unitarity equations involving 2 → 2, 2 → 3, and 3 → 3 processes is given when the total (including all disconnected processes) 3 → 3 partial-wave amplitude $S$ is non-normal. The solution is given in terms of characteristic operator functions, using the theory of completely nonunitary operators. It is shown, once the characteristic operator function is given, how to compute the 2 → 3 partial-wave amplitude. An appendix shows that, if $S$ can be exponentiated and all forces are two-body forces, no particle production is allowed, i.e., the 2 → 3 partial-wave amplitude is zero.

• Received 18 December 1972

DOI:https://doi.org/10.1103/PhysRevD.7.2989