Erratum: Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED \newline [Phys. Rev. D 96, 036021 (2017)]

TL;DR

This paper formulates and solves the fermion propagator Schwinger-Dyson equation in Minkowski space using spectral representation and on-shell renormalization, providing explicit solutions with correct analytic structure in quenched QED.

Contribution

It introduces a spectral representation approach to solve the fermion propagator SDE in Minkowski space with on-shell renormalization in quenched QED, offering explicit solutions.

Findings

Explicit spectral functions for the fermion propagator obtained.

Solutions demonstrate correct analytic structure of the propagator.

Method provides a guiding example despite model limitations.

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, numeric solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique Ansatz for the fermion-photon vertex in the quenched approximation in the Yennie gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure.