Dimensionally regularized study of nonperturbative quenched QED

Abstract

We study the dimensionally regularized fermion propagator Dyson-Schwinger equation in quenched nonperturbative QED in an arbitrary covariant gauge. The nonperturbative fermion propagator is solved in $D\ensuremath{\equiv}4\ensuremath{-}2\ensuremath{\epsilon}<4$ dimensional Euclidean space for a large number of values of $\ensuremath{\epsilon}.$ Results for $D=4$ are then obtained by the extrapolation $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\epsilon}}0.$ The nonperturbative renormalization is performed numerically, yielding finite results for all renormalized quantities. This demonstrates, apparently for the first time, that it is possible to successfully implement nonperturbative renormalization of Dyson-Schwinger equations within a gauge invariant regularization scheme such as dimensional regularization. Here we present results using the Curtis-Penningon fermion-photon proper vertex for two values of the coupling, namely $\ensuremath{\alpha}=0.6$ and $\ensuremath{\alpha}=1.5$, and compare these to previous studies employing a modified ultraviolet cut-off regularization. The results using the two different regularizations are found to agree to within the numerical precision of the present calculations.