Diagrammatic Cancellations and the Gauge Dependence of QED

TL;DR

This paper investigates how diagrammatic cancellations in QED across different gauges can be used to understand gauge dependence of the electron propagator, employing Dyson-Schwinger equations and dimensional regularization.

Contribution

It introduces a method to reconstruct gauge dependence in QED from a specific gauge result using diagrammatic cancellations and Dyson-Schwinger equations.

Findings

Demonstrates 3-loop epsilon-expansion in Feynman gauge determines gauge-dependent terms up to 4 loops.

Uses dimensional regularization to connect gauge dependence across loop orders.

Provides a systematic approach to gauge dependence in QED calculations.

Abstract

This letter examines diagrammatic cancellations for Quantum Electrodynamics (QED) in the general linear gauge. These cancellations combine Feynman graphs of various topologies and provide a method to reconstruct the gauge dependence of the electron propagator from the result of a particular gauge by means of a linear Dyson-Schwinger equation. We use this method in combination with dimensional regularization to demonstrate how the 3-loop ${\epsilon}$-expansion in the Feynman gauge determines the ${\epsilon}$-expansions for all gauge parameter dependent terms to 4 loops.