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

## TL;DR

This paper investigates chiral symmetry breaking in quenched strong-coupling QED4 using Dyson-Schwinger equations, comparing different vertex Ansätze and analyzing gauge dependence with implications for lattice studies.

## Contribution

It implements a numerical renormalization program for Dyson-Schwinger equations in quenched QED4 and compares three vertex Ansätze to understand chiral symmetry breaking.

## Key findings

- Renormalized axial current is conserved in the chiral limit.
- Numerical method is stable and straightforward to implement.
- Gauge dependence varies with vertex choice, affecting results.

## Abstract

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.