Hopf-algebraic Renormalization of QED in the linear covariant Gauge

Abstract

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green's functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.

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Cited by in corpus (4)

• Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultra-relativistic limit of Dirac liquids
• Diagrammatic Cancellations and the Gauge Dependence of QED
• Log-Expansions from Combinatorial Dyson-Schwinger Equations
• Six dimensional ultraviolet completion of the $CP(N)$ $\sigma$ model at two loops