How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex

M.R. Pennington; Shaoyang Jia

How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex

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arxiv 1610.10049 v2 pith:RUDEHBQQ submitted 2016-10-31 nucl-th

Shaoyang Jia , M.R. Pennington This is my paper · ORCID

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keywords gaugecovariancefermionrequirementdimensionsensurespropagatorsadditionally

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We derive the gauge covariance requirement imposed on the QED fermion-photon three-point function within the framework of a spectral representation for fermion propagators. When satisfied, such requirement ensures solutions to the fermion propagator Schwinger-Dyson equation (SDE) in any covariant gauge with arbitrary numbers of spacetime dimensions to be consistent with the Landau-Khalatnikov-Fradkin transformation (LKFT). The general result has been verified by the special cases of three and four dimensions. Additionally, we present the condition that ensures the vacuum polarization is independent of the gauge parameter. As an illustration, we show how the Gauge Technique dimensionally regularized in 4D does not satisfy the covariance requirement.

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Erratum: Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED \newline [Phys. Rev. D 96, 036021 (2017)]
nucl-th 2024-12 conditional novelty 5.0 of 10

The paper corrects its earlier Landau-gauge result: quenched QED with the modified Gauge Technique vertex allows on-shell renormalization only in the Yennie gauge (ξ=3), where consistent spectral-function solutions exist.

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