We study the gauge covariance of the massive fermion propagator in three as well as four-dimensional quantum electrodynamics (QED). Starting from its value at the lowest order in perturbation theory, we evaluate a nonperturbative expression for it by means of its Landau-Khalatnikov-Fradkin (LKF) transformation. We compare the perturbative expansion of our findings with the known one-loop results and observe perfect agreement up to a gauge parameter independent term, a difference permitted by the structure of the LKF transformations.

• Received 26 June 2002

DOI:https://doi.org/10.1103/PhysRevD.66.105005