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.