Study of relativistic bound states for scalar theories in the Bethe-Salpeter and Dyson-Schwinger formalism

The Bethe-Salpeter equation for Wick-Cutkosky-like models is solved in the dressed ladder approximation. The bare vertex truncation of the Dyson-Schwinger equations for propagators is combined with the dressed ladder Bethe-Salpeter equation for the scalar S-wave bound state amplitudes. With the help of the spectral representation the results are obtained directly in Minkowski space. We give a new analytic formula for the resulting equation simplifying the numerical treatment. The bare ladder approximation of the Bethe-Salpeter equation is compared with the one with dressed ladder. The elastic electromagnetic form factors are calculated within the relativistic impulse approximation.