Gauge covariance of the fermion Schwinger-Dyson equation in QED

Abstract

Any practical application of the Schwinger-Dyson equations to the study of $n$-point Green's functions of a field theory requires truncations, the best known being finite order perturbation theory. Strong coupling studies require a different approach. In the case of QED, gauge covariance is a powerful constraint. By using a spectral representation for the massive fermion propagator in QED, we are able to show that the constraints imposed by the Landau-Khalatnikov-Fradkin transformations are linear operations on the spectral densities. Here we formally define these group operations and show with a couple of examples how in practice they provide a straightforward way to test the gauge covariance of any viable truncation of the Schwinger-Dyson equation for the fermion 2-point function.

arXiv comment6 pages, 3 figures

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Cited by in corpus (9)

• Transverse Takahashi Identities and Their Implications for Gauge Independent Dynamical Chiral Symmetry Breaking
• Landau-Khalatnikov-Fradkin transformation and the mystery of even $\zeta$-values in Euclidean massless correlators
• Exact Solutions to the Fermion Propagator Schwinger-Dyson Equation in Minkowski space with on-shell Renormalization for Quenched QED
• A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations
• Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED
• Diagrammatic Cancellations and the Gauge Dependence of QED
• Landau-Khalatnikov-Fradkin Transformations, Nielsen Identities, Their Equivalence and Implications for QCD
• Landau-Khalatnikov-Fradkin transformations for the two loop massless quark propagator
• Direct solution of Minkowski-space Bethe-Salpeter equation in the massive Wick-Cutkosky model