Gauge covariant approximations in scalar electrodynamics

In electrodynamics the longitudinal components of all charged-particle Green functions are determined by the charged-particle propagator. Inserting these components into the Dyson-Schwinger equation leads to an integral equation for the propagator itself which may be solved and used as a basis for an iterative determination of the transverse Green functions' components. The solution for electrodynamics of scalar mesons is found in analogy with recent work on spinor electrodynamics.