Exact Solutions to the Fermion Propagator Schwinger-Dyson Equation in Minkowski space with on-shell Renormalization for Quenched QED
arXiv:1705.04523 · doi:10.1103/PhysRevD.96.036021
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 Padé approximation for the spectral functions is also investigated.
12 pages, 3 figures