A dynamical model for pion electroproduction on the nucleon

We develop a Lorenz- and gauge-invariant dynamical model for pion electroproduction in the resonance region. The model is based on solving of the Salpeter (instantaneous) equation for the pion-nucleon interaction with a hadron-exchange potential. We find that the one-particle-exchange kernel of the Salpeter equation for pion electroproduction develops an unphysical singularity for a finite value of $Q^{2}$. We analyse two methods of dealing with this problem. Results of our model are compared with recent single-polarization data for pion electroproduction.