Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched QED

Abstract

We study the gauge covariance of the massless fermion propagator in three-dimensional quenched quantum electrodynamics in the framework of dimensional regularization in $d=3\ensuremath{-}2ϵ$. Assuming the finiteness of the quenched perturbative expansion, that is the existence of the limit $ϵ\ensuremath{\rightarrow}0$, we state that, exactly in $d=3$, all odd perturbative coefficients, starting with the third order one, should be zero in any gauge.