Chiral Symmetry Breaking in Strongly Coupled Quenched QED${}_4$ Using the Dyson-Schwinger Equation Formalism

We study chiral symmetry breaking in quenched strong-coupling QED${}_4$ in arbitrary covariant gauge within the Dyson-Schwinger equation formalism. A recently developed numerical renormalization program is fully implemented. Results are compared for three different fermion-photon proper vertex {\it Ans"{a}tze/}: bare ${\gamma }^{\mu }$, minimal Ball-Chiu, and Curtis-Pennington. The procedure is straightforward to implement and numerically stable. We discuss the chiral limit and observe that in this limit the renormalized axial current is conserved. A detailed study of residual gauge dependence due to the vertex choice is in progress. The relevance for lattice studies is discussed.