Minkowski-space solutions of the Schwinger-Dyson equation for the fermion propagator with the rainbow-ladder truncation

TL;DR

This paper presents a method for solving the Minkowski-space Schwinger-Dyson equation for the fermion propagator in QED with massive photons, revealing its analytic structure and enabling future calculations of Bethe-Salpeter amplitudes.

Contribution

It introduces a novel approach to solving the Minkowski-space SDE for the fermion propagator with massive photons, including regularization and analysis of analytic structure.

Findings

Fermion propagator has an on-shell pole and timelike branch cuts.

Method is consistent with complex momentum solutions.

Lays groundwork for Minkowski-space Bethe-Salpeter calculations.

Abstract

We solve the Minkowski-space Schwinger-Dyson equation (SDE) for the fermion propagator in quantum electrodynamics (QED) with massive photons. Specifically, we work in the quenched approximation within the rainbow-ladder truncation. Loop-divergences are regularized by the Pauli-Villars regularization. With moderately strong fermion-photon coupling, we find that the analytic structure of the fermion propagator consists of an on-shell pole and branch-cuts located in the timelike region. Such structures are consistent with the direct solution of the fermion propagator as functions of the complex momentum. Our method paves the way towards the calculation of the Minkowski-space Bethe-Salpeter amplitude using dressed fermion propagator.