Bound state solutions of scalar QED_{2+1} for zero photon mass

The Feynman-Schwinger representation is used to study the behavior of solutions of scalar QED in (2+1) dimensions. The limit of zero photon mass is seen to be smooth. The Bethe-Salpeter equation in the ladder approximation also exhibits this property. They clearly deviate from the behavior in the nonrelativistic limit. In a variational analysis we show that this difference can be attributed to retardation effects of relativistic origin.