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.

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• On the self-consistency of off-shell Slavnov-Taylor identities in QCD
• Gauge covariance of the fermion Schwinger-Dyson equation in QED
• Gauge Symmetries and Renormalization
• The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators
• Six dimensional ultraviolet completion of the $CP(N)$ $\sigma$ model at two loops
• Off-shell Diagrammatics for Quantum Gravity
• Non-perturbative gauge transformations of arbitrary fermion correlation functions in quantum electrodynamics
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