Non-perturbative Fermion Propagator for the Massless Quenched QED3

TL;DR

This paper derives a non-perturbative fermion propagator for massless quenched QED3 using Landau-Khalatnikov-Fradkin transformations, matching two-loop perturbative results and emphasizing the importance of vertex construction.

Contribution

It provides a non-perturbative expression for the fermion propagator in quenched QED3 that aligns with two-loop perturbation theory, guiding vertex modeling in Schwinger-Dyson equations.

Findings

The non-perturbative propagator matches two-loop perturbative expansion.

Comparison shows the non-perturbative result differs from one-loop approximations.

Plots in different gauges illustrate the propagator's behavior across regimes.

Abstract

For massless quenched QED in three dimensions, we evaluate a non-perturbative expression for the fermion propagator which agrees with its two loop perturbative expansion in the weak coupling regime. This calculation is carried out by making use of the Landau-Khalatnikov-Fradkin transformations. Any improved construction of the fermion-boson vertex must make sure that the solution of the Schwinger-Dyson equation for the fermion propagator reproduces this result. For two different gauges, we plot the fermion propagator against momentum. We then make a comparison with a similar plot, using the earlier expression for the fermion propagator, which takes into account only the one loop result.