Fermion Propagator in Quenched QED3 in the Light of the Landau-Khalatnikov-Fradkin Tranformation

We study the gauge dependence of the fermion propagator in quenched QED3, with and without dynamical symmetry breaking, in the light of its Landau-Khalatnikov-Fradkin transformation (LKFT). In the former case, starting with the massive bare propagator in the Landau gauge, we obtain non perturbative propagator in an arbitrary covariant gauge. Carrying out a perturbative expansion of this result, it yields correct wavefunction renormalization and the mass function up to the terms independent of the gauge parameter. Also, we obtain valuable information for the higher order perturbative expansion of the propagator. As for the case of dynamical chiral symmetry breaking, we start by approximating the numerical solution in Landau gauge in the rainbow approximation in terms of analytic functions. We then use LKFT to obtain the dynamically generated fermion propagator in an arbitrary covariant gauge. We find that the results obtained have all the required qualitative features. We also go beyond the rainbow and encounter similar desirable qualitative features.