On the gauge dependence of Quantum Electrodynamics

TL;DR

This paper presents a diagrammatic, perturbative method to analyze gauge dependence in Quantum Electrodynamics, enabling the expansion of Green's functions across gauges and clarifying the relation with the Landau-Khalatnikov-Fradkin transform.

Contribution

It introduces a dimensionally independent, purely perturbative technique to construct Green's functions' gauge parameter expansion in QED.

Findings

Developed a diagrammatic approach for gauge dependence analysis.

Established the compatibility of perturbation theory with the Landau-Khalatnikov-Fradkin transform.

Provided a full expansion of Green's functions in gauge parameters.

Abstract

This paper reports on our diagrammatic approach to characterize the gauge dependence of Quantum Electrodynamics in the linear covariant gauge. Our dimensionally independent technique is purely based on a perturbative analysis and allows us to construct the full expansion in the gauge~parameter of a Green's function from its value in a particular gauge (such as the Feynman or Landau gauge). Further, we clarify the compatiblity of perturbation theory and the Landau-Khalatnikov-Fradkin transform.