Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

TL;DR

This paper investigates the gauge-covariance of the massless fermion propagator in reduced QED using the Landau-Khalatnikov-Fradkin transformation, confirming weak coupling expansions and gauge invariance of the fermion anomalous dimension.

Contribution

It provides an all-order expression for the fermion propagator in different gauges and proves gauge invariance of the fermion anomalous dimension beyond the first order in reduced QED.

Findings

Weak coupling expansions match exact calculations.

Fermion anomalous dimension is gauge invariant to all orders except the first.

All-order transformation of the fermion propagator in different gauges.

Abstract

We study the gauge-covariance of the massless fermion propagator in reduced Quantum Electrodynamics (QED). Starting from its value in some gauge, we evaluate an all order expression for it in another gauge by means of the Landau-Khalatnikov-Fradkin transformation. We find that the weak coupling expansions thus derived are in perfect agreement with the exact calculations. We also prove that the fermion anomalous dimension of reduced QED is gauge invariant to all orders of perturbation theory except for the first one.