In the quenched approximation, the gauge covariance properties of three
vertex Ans\"{a}tze in the Schwinger-Dyson equation for the fermion self energy
are analysed 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 Ansatz can confer gauge covariance upon the Schwinger-Dyson
equation is presented and the Curtis and Pennington 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.Comment: 17 pages, PHY-7143-TH-93, REVTE