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arXiv · 1610.06001

Gauge covariance of the fermion Schwinger-Dyson equation in QED

Shaoyang Jia·M. R. Pennington
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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.

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Shaoyang Jia, M. R. Pennington. 2016-10-19. Gauge covariance of the fermion Schwinger-Dyson equation in QED. https://doi.org/10.1016/j.physletb.2017.03.032

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