Toward an exact quantum electrodynamics

The dimensionally regularized and renormalized Dyson equations for the true fermion propagator are solved by an iteration procedure which determines the gauge-invariant true vertex part up to a single parameter by requiring, after algebraic elimination of the true photon propagator, that the vacuum polarization integral and the self-energy integral be free of infinities in the dimensional limit, and that the vacuum polarization exhibit positronium resonances at the appropriate thresholds. There is no infrared catastrophe. The results of the first iteration are compatible with the results of second-order renormalized perturbation theory.