Fermion Propagator in Quenched QED3 in the light of the Landau-Khalatnikov-Fradkin transformation

TL;DR

This paper investigates the gauge dependence of the fermion propagator in quenched QED3 using the Landau-Khalatnikov-Fradkin transformation, providing nonperturbative insights and extending results to cases with dynamical chiral symmetry breaking.

Contribution

It introduces a nonperturbative method to obtain fermion propagators in arbitrary gauges from Landau gauge solutions, including cases with dynamical symmetry breaking, using LKFT.

Findings

Exact wavefunction renormalization at one-loop level.

Qualitative features of the dynamical chiral symmetry breaking propagator.

Extension of LKFT to improved vertex ansätze.

Abstract

We study the gauge dependence of the fermion propagator in quenched QED3 with and without dynamical symmetry breaking in the light of its Landau-Khalatnikov-Fradkin Transformation (LKFT). In the former case, starting with the massive bare propagator in the Landau gauge, we obtain non perturbative propagator in an arbitrary covariant gauge. At the one-loop level it yields exact wavefunction renormalization and correct $(\alpha \xi)$ terms for the mass fuction. Also, we obtain valuable information for the higher order perturbative expansion of the propagator. As for the case of dynamical chiral symmetry breaking, we start by approximating the numerical solution to the Schwinger-Dyson equation in Landau gauge in the rainbow approximation in terms of analytic functions. We then LKF transform this result to obtain the dynamically generated fermion propagator in an arbitrary covariant gauge. We find that the results obtained have nice qualitative features. We also extend this exercise to the cases involving more reliable ans\"atze for the vertex and encounter similar (and improved) qualitative features.