Gauge covariance and the fermion-photon vertex in three- and four-dimensional, massless quantum electrodynamics.

In the quenched approximation, the gauge covariance properties of three vertex [ital Ansa]$[ital iuml]---[ital tze] in the Schwinger-Dyson equation for the fermion self-energy are analyzed in three- and four-dimensional quantum electrodynamics. Based on the Cornwall-Jackiw-Tomboulis effective action, it is inferred that the spectral representation used for the vertex in the gauge technique cannot support dynamical chiral symmetry breaking. A criterion for establishing whether a given [ital Ansatz] can confer gauge covariance upon the Schwinger-Dyson equation is presented and the Curtis and Pennington [ital Ansatz] is shown to satisfy this constraint. We obtain an analytic solution of the Schwinger-Dyson equation for quenched, massless three-dimensional quantum electrodynamics for arbitrary values of the gauge parameter in the absence of dynamical chiral symmetry breaking.