Does the weak coupling limit of the Burden-Tjiang deconstruction of the massless quenched QED3 vertex agree with perturbation theory?

TL;DR

This paper investigates whether the non-perturbative fermion-boson vertex in massless QED3 aligns with perturbative results at order α, highlighting the need for a vertex model consistent with perturbation theory.

Contribution

It derives constraints on the non-perturbative vertex in QED3 from perturbative calculations and evaluates the fermion propagator to compare with existing conjectures.

Findings

Perturbative calculations at order α are consistent with the derived constraints.

The Burden-Tjiang conjecture shows drawbacks when compared to perturbative results.

A non-perturbative vertex form that matches the perturbative limit is necessary.

Abstract

We derive constraints on the non-perturbative 3-point fermion-boson transverse vertex in massless QED3 from its perturbative calculation to order $\alpha$. We also check the transversality condition to two loops and evaluate the fermion propagator to the same order. We compare a conjecture of the non-perturbative vertex by Burden and Tjiang against our results and comment on its draw backs. Our calculation calls for the need to construct a non-perturbative form for the fermion-boson vertex which agrees with its perturbative limit to ${\cal O}(\alpha)$.