Electron-Photon Vertex and Dynamical Chiral Symmetry Breaking in Reduced QED: An Advanced Study of Gauge Invariance

TL;DR

This paper develops a refined electron-photon vertex model in reduced QED that respects symmetries and asymptotic limits, enabling the study of dynamical chiral symmetry breaking and demonstrating gauge independence of key quantities.

Contribution

It introduces a new vertex ansatz satisfying symmetry and perturbative constraints, improving the understanding of chiral symmetry breaking in reduced QED.

Findings

Dynamically generated electron mass follows Miransky scaling.

Gauge dependence of critical parameters is minimized within a specific gauge interval.

The vertex ansatz ensures multiplicative renormalizability of the electron propagator.

Abstract

We study the effect of a refined electron-photon vertex on the dynamical breaking of chiral symmetry in reduced quantum electrodynamics. We construct an educated {\em ansatz} for this vertex which satisfies the required discrete symmetries under parity, time reversal and charge conjugation operations. Furthermore, it reproduces its asymptotic perturbative limit in the weak coupling regime and ensures the massless electron propagator is multiplicatively renormalizable in its leading logarithmic expansion. Employing this vertex {\em ansatz}, we solve the gap equation to compute dynamically generated electron mass whose dependence on the electromagnetic coupling is found to satisfy Miransky scaling law. We also investigate the gauge dependence of this dynamical mass as well as that of the critical coupling above which chiral symmetry is dynamically broken. As a litmus test of our vertex construction, both these quantities are rendered virtually gauge independent within a certain interval of values considered for the covariant gauge parameter.