Nonperturbative study of the fermion propagator in quenched QED in covariant gauges using a renormalizable truncation of the Schwinger-Dyson equation

The Schwinger-Dyson equation for the fermion propagator in quenched four-dimensional QED is solved using a nonperturbative ansatz for the fermion-photon vertex that satisfies the Ward-Takahashi identity, ensures the multiplicative renormalizability of the fermion equation, and reproduces low-order perturbation theory in the appropriate limit. The fermion propagator then possesses a chiral-symmetry-breaking phase only when the coupling $\alpha$ is larger than a critical value ${\alpha }_c\simeq 0.92$. This critical coupling is almost exactly gauge independent as is the dynamically generated mass, in complete contrast to the popular rainbow approximation.