A gauge covariant approximation to quantum electrodynamics

A non-perturbative method of solving the Dyson-Schwinger equations in QED, which preserves the gauge identities, is considered. The starting point is determined by an integral equation for the electron propagator spectral function which is explicitly solved in the Landau gauge; this determines the Green functions in successive orders of iteration since no spurious infinities arise beyond the usual renormalizable ones.