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

Abstract

We derive constraints on the non-perturbative 3-point fermion-boson transverse vertex in massless QED3 from its perturbative calculation to order α. 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 drawbacks. Our calculation calls for the need to construct a non-perturbative form for the fermion-boson vertex which agrees with its perturbative limit to O(α).