Direct Bethe-Salpeter solutions in Minkowski space

Abstract

We review a method to directly solve the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the many singularities which appear in the kernel and propagators. The off-mass shell scattering amplitude for spinless particles interacting by a one boson exchange was computed for the first time. Using our Minkowski space solutions for the initial (bound) and final (scattering) states, we calculate elastic and transition (bound → scattering state) electromagnetic form factors. The conservation of the transition electromagnetic current J · q = 0, verified numerically, confirms the validity of our solutions.