Three-particle equations for the coupled N-N system

An analysis of the coupled N-N system is carried out using the Hamiltonian of the Chew-Low theory. This Hamiltonian describes the interaction of pions with a static nucleon through the virtual process NN+. A set of three-particle equations is obtained whose solutions satisfy two-and three-particle unitarity, as well as the discontinuity relations for the production amplitudes (N+N+2 in the subenergy variables, i.e., the energy of one of the final state pions. It is shown that in order to satisfy the subenergy discontinuity relation, it is necessary to include all four P-wave -N amplitudes as input to the three-particle equations. In particular, even though the is not an elementary particle in the model considered, its amplitude must be part of the input. The analysis presented shows how to modify the standard three-particle equations to account for single nucleon intermediate states. An expansion for the production amplitude similar to the isobar expansion emerges from the analysis. An approximation for the nucleon propagator is obtained which includes the effect of two meson states.