On the occurrence of particle-antiparticle resonances in scalar QED

We derive a relativistic two-body wave equation from scalar QED (the Wick-Cutkosky model) in the one-photon exchange approximation, using a technique proposed earlier for QED. This involves the study of the equation of motion for a matrix element of the 'electron' field operator between a state with two particles and another with one particle, and the application of well defined approximations. We study the L=0 partial wave in some detail. Using a complex scaling technique we show that within the current approximation no resonances are found that can explain the long-lived states observed in heavy-ion scattering at the GSI. We comment on other calculations that have reported positive results for the same problem. (orig.)