Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched QED

TL;DR

This paper investigates the gauge-covariance of the massless fermion propagator in three-dimensional quenched QED using dimensional regularization, revealing that all odd perturbative coefficients vanish in the physical dimension.

Contribution

It demonstrates that in three-dimensional quenched QED, all odd-order perturbative coefficients of the fermion propagator are zero, assuming the finiteness of the perturbative expansion.

Findings

All odd perturbative coefficients vanish in d=3.

The analysis is based on the assumption of the finiteness of the quenched perturbative series.

The study uses dimensional regularization to analyze gauge-covariance.

Abstract

We study the gauge-covariance of the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics in the framework of dimensional regularization in d=3-2\ep. Assuming the finiteness of the quenched perturbative expansion, that is the existence of the limit \ep \to 0, we state that, exactly in d=3, all odd perturbative coefficients, starting with the third order one, should be zero in any gauge.