Gauge dependence of mass and condensate in chirally asymmetric phase of quenched three-dimensional QED

We study three-dimensional quenched quantum electrodynamics in the bare vertex approximation. We investigate the gauge dependence of the dynamically generated Euclidean mass of the fermion and the chiral condensate for a wide range of values of the covariant gauge parameter $\ensuremath{\xi}.$ We find that (i) away from the Landau gauge toward large positive values of $\ensuremath{\xi},$ the gauge dependence of the said quantities is considerably reduced without resorting to sophisticated vertex Ans\"atze, (ii) wave function renormalization plays an important role in restoring gauge invariance, and (iii) the Ward-Green-Takahashi identity seems to increase the gauge dependence when used in conjunction with some simplifying assumptions. In the Landau gauge, we also verify that our results are in agreement with those based upon the dimensional regularization scheme within the numerical accuracy available.