%0 Journal Article
%T Gauge covariance and the fermion-photon vertex in three- and four- dimensional, massless quantum electrodynamics
%A Conrad J. Burden
%A Craig D. Roberts
%J Physics
%D 1993
%I arXiv
%R 10.1103/PhysRevD.47.5581
%X 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.
%U http://arxiv.org/abs/hep-th/9303098v1