Shaoyang Jia

College of William and Mary, Williamsburg, VA

Gauge covariance of the Schwinger-Dyson equations for QED propagators in Minkowski space

The dependence of the QED fermion propagator on the covariant gauge fixing conditions was originally formulated by the Landau-Khalatnikov-Fradkin transform (LKFT) in coordinate space. After introducing a spectral representation, the gauge dependence of the fermion propagator in momentum space is solved exactly with arbitrary numbers of spacetime dimensions. The necessary and sufficient condition to ensure the gauge covariance of solutions for each propagator Schwinger-Dyson equation (SDE) has been derived. This paves a path to the gauge covariant truncation of the SDEs and their solutions in Minkowski space.

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