Does the weak coupling limit of the Burden-Tjiang deconstruction of the massless quenched three-dimensional QED vertex agree with perturbation theory? art. no. 085002

We derive constraints on the non-perturbative 3-point fermion-boson transve rse vertex in massless QED3 from its perturbative calculation to order alph a. 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-p erturbative vertex by Burden and Tjiang against our results and comment on its drawbacks. Our calculation calls for the need to construct a non-pertur bative form for the fermion-boson vertex which agrees with its perturbative limit to O(alpha).