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

Abstract

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.

14 pages, 5 figures

References in corpus (4)

• Building the Full Fermion-Photon Vertex of QED by Imposing Multiplicative Renormalizability of the Schwinger-Dyson Equations for the Fermion and Photon Propagators
• $\bar{q}q$ condensate for light quarks beyond the chiral limit
• Numerical Investigation of Fermion Mass Generation in QED
• Critical Number of Flavours in QED

Cited by in corpus (5)

• Non-perturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges: Nielsen identities and a BRST invariant two-point correlation function
• Exact Solutions to the Fermion Propagator Schwinger-Dyson Equation in Minkowski space with on-shell Renormalization for Quenched QED
• Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED
• Gauge covariance of the fermion Schwinger-Dyson equation in QED
• Dynamical Chiral Symmetry Breaking in Quantum Chromo Dynamics: Delicate and Intricate