Gauge invariance and Compton scattering from relativistic composite systems

Using the Ward-Takahashi (WT) identity and the Bethe-Salpeter wave equation, we investigate the dynamical requirements imposed by electromagnetic gauge invariance on Compton scattering from relativistic composite systems. The importance of off-shell rescattering in intermediate states, which is equivalent to final state interactions in inclusive processes, is clarified in the context of current conservation. It is shown that, if the nuclear force is nonlocal, there will be both two-photon interaction currents and rescattering contributions to terms involving one-photon interaction currents. We derive the two-body WT identity for the two-photon interaction currents, and obtain explicit forms for the interaction current operators for three illustrative models of nuclear forces: (a) two-pion exchange forces with baryon resonances, (b) covariant separable forces, and (c) charged one-pion exchange