Confinement and the analytic structure of the one-body propagator in scalar QED - art. no. 116006

We investigate the behavior of the one-body propagator in SQED. The self-en ergy is calculated using three different methods: (i) the simple bubble sum mation, (ii) the Dyson-Schwinger equation, and (iii) the Feynman-Schwinger representation. The Feynman-Schwinger representation allows an exact analyt ical result. It is shown that, while the exact result produces a real mass pole for all couplings, the bubble sum and the Dyson-Schwinger approach in the rainbow approximation lead to complex mass poles beyond a certain criti cal coupling. The model exhibits confinement, yet the exact solution still has one-body propagators with real mass poles.