Four-loop singularities of the massless fermion propagator in quenched three-dimensional QED

TL;DR

This paper computes three- and four-loop corrections to the massless fermion propagator in quenched 3D QED, revealing gauge-dependent singularities at four loops and confirming the Landau-Khalatnikov-Fradkin transformation.

Contribution

It provides explicit four-loop calculations of the fermion propagator in quenched 3D QED, highlighting gauge invariance and singularities, and confirms known gauge transformation properties.

Findings

Three-loop correction is finite and gauge invariant.

Four-loop correction has singularities except in Feynman gauge.

Gauge-dependent terms are determined by lower order terms, consistent with known transformations.

Abstract

We calculate the three- and four-loop corrections to the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics with four-component fermions. The three-loop correction is finite and gauge invariant but the four-loop one has singularities except in the Feynman gauge where it is also finite. Our results explicitly show that, up to four loops, gauge-dependent terms are completely determined by lower order ones in agreement with the Landau-Khalatnikov-Fradkin transformation.