Non-perturbative fermion propagator for the massless quenched QED3

For massless quenched QED in three dimensions, we evaluate a non-perturbati ve expression for the fermion propagator which agrees with its two loop per turbative expansion in the weak coupling regime. This calculation is carrie d out by making use of the Landau-Khalatnikov-Fradkin transformations. Any improved construction of the fermion-boson vertex must make sure that the s olution of the Schwinger-Dyson equation for the fermion propagator reproduc es this result. For two different gauges, we plot the fermion propagator ag ainst momentum. We then make a comparison with a similar plot, using the ea rlier expression for the fermion propagator, which takes into account only the one loop result. (C) 2000 Published by Elsevier Science B.V.