Nucleon-nucleon scattering above the pion production threshold

Starting from a simple nonrelativistic field theory of pions and nucleons, we derive linear integral equations coupling amplitudes of baryon number equal two systems. These equations guarantee two- and three-body unitarity above the threshold for single pion production, and include explicity the coupling of the $\mathrm{NN}$ to (e.g.) $N\Delta$ and $\pi d$ channels. The relationship of this approach to earlier schemes is discussed.