Dynamical mass generation in unquenched QED using the Dyson--Schwinger equations

TL;DR

This paper conducts a detailed numerical analysis of dynamical mass generation in unquenched QED using Dyson--Schwinger equations, evaluating the effectiveness of the KP vertex ansatz and its gauge-variance issues.

Contribution

It introduces a comprehensive unquenched QED study with a new fermion-antifermion-boson interaction ansatz, comparing its performance against existing vertices.

Findings

The KP vertex shows incomplete gauge invariance due to missing massive transverse components.

Unquenched QED exhibits critical behavior in dynamical mass generation.

The KP vertex's gauge-variance is comparable to hybrid vertices with the Curtis--Pennington vertex.

Abstract

We present a comprehensive numerical study of dynamical mass generation for unquenched QED in four dimensions, in the absence of four-fermion interactions, using the Dyson--Schwinger approach. We begin with an overview of previous investigations of criticality in the quenched approximation. To this we add an analysis using a new fermion-antifermion-boson interaction ansatz, the Kizilersu-Pennington (KP) vertex, developed for an unquenched treatment. After surveying criticality in previous unquenched studies, we investigate the performance of the KP vertex in dynamical mass generation using a renormalized fully unquenched system of equations. This we compare with the results for two hybrid vertices incorporating the Curtis--Pennington vertex in the fermion equation. We conclude that the KP vertex is as yet incomplete, and its relative gauge-variance is due to its lack of massive transverse components in its design.