A gauge covariant approximation to QED

TL;DR

This paper develops a gauge covariant approximation for the fermion propagator in quenched QED, using spectral representation and vertex ansatz to preserve Ward-Takahashi Identity, leading to analytic solutions and insights into chiral symmetry breaking.

Contribution

It introduces a spectral representation approach with a vertex ansatz that maintains gauge invariance in quenched QED, providing analytic solutions in four dimensions and smoothing threshold behaviors.

Findings

Avoids infrared singularity in three dimensions

Provides analytic solutions in terms of hypergeometric functions in four dimensions

Indicates possible dynamical chiral symmetry breaking in four-dimensional QED

Abstract

We examine the Dyson-Schwinger equation for the fermion propagator in quenched QED in three and four dimension based on spectral representation with vertex ansatz which preserves Ward-Takahashi Identity.An appropriate renormalization within dispersion integral smoothes the threshold behaviour of the fermion self energy in three dimension.Thus we avoid the infrared singurality in three dimension.The behaviour of the fermion propagator in three dimension near the threshold is then found to be similar to the four dimensional one.There exisit analytic solutions for arbitrary gauges and the full propagators are expressed in terms of hypergeometric function in four dimension.There is a possibility of dynamical chiral symmetry breaking in four dimension with vanishing bare mass.