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arXiv · 1705.04523

Exact Solutions to the Fermion Propagator Schwinger-Dyson Equation in Minkowski space with on-shell Renormalization for Quenched QED

Shaoyang Jia·M. R. Pennington
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Abstract

With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Pad\'{e} approximation for the spectral functions is also investigated.

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Shaoyang Jia, M. R. Pennington. 2017-05-12. Exact Solutions to the Fermion Propagator Schwinger-Dyson Equation in Minkowski space with on-shell Renormalization for Quenched QED. https://doi.org/10.1103/physrevd.96.036021

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