Scattering and Production Amplitudes with Unstable Particles

An S-matrix theory is developed for a system of strongly interacting particles in which unstable particles are included. The particular system considered is π+N↔π+N, π+N↔ρ+N, and ρ+N↔ρ+N. Only the one-pion-exchange interaction is included. The relationship to the strip approximation and the application to the higher resonances in pion-nucleon scattering are discussed. Complex singularities are evaluated, and their relationship to the generalized unitarity condition for the pion-pion system is stressed. An extended ND^-1 method is used to develop a system of nonsingular, uncoupled, Fredholm integral equations, from which the transition amplitudes can be evaluated.