Non-perturbative Fermion Propagator for the Massless Quenched QED3

For massless quenched QED in three dimensions, we evaluate a non-perturbative expression for the fermion propagator which agrees with its two loop perturbative expansion in the weak coupling regime. This calculation is carried out by making use of the Landau-Khalatnikov-Fradkin transformations. Any improved construction of the fermion-boson vertex must make sure that the solution of the Schwinger-Dyson equation for the fermion propagator reproduces this result. For two different gauges, we plot the fermion propagator against momentum. We then make a comparison with a similar plot, using the earlier expression for the fermion propagator, which takes into account only the one loop result.