Diagrammatic Cancellations and the Gauge Dependence of QED

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.

References in corpus (5)

• The Hopf algebra of Feynman graphs in QED
• Gauge covariance of the fermion Schwinger-Dyson equation in QED
• Gauge-Dependence of Green's Functions in QCD and QED
• FORM, Diagrams and Topologies
• Renormalizable Expansion for Nonrenormalizable Theories: II. Gauge Higher Dimensional Theories

Cited by in corpus (3)

• Gauge covariance of the fermion Schwinger-Dyson equation in QED
• The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators
• Non-perturbative gauge transformations of arbitrary fermion correlation functions in quantum electrodynamics