On Landau-Khalatnikov-Fradkin transformation in quenched QED3

We present the results of studies [1,2] of the gauge covariance of the massless fermion propagator in three-dimensional quenched quantum electrodynamics in the framework of dimensional regularization in d=3-2\ep. Assuming the finiteness of the perturbative expansion, i.e. existence of the limit \ep \to 0, it was shown in [1] that exactly for d=3 all odd perturbative coefficients, starting from the third order, must be equal to zero in any gauge. To test this, in Ref. [2] we calculated three- and four-loop corrections to the massless fermionic propagator. Three-loop corrections are finite and gauge-invariant, while four-loop corrections have singularities. The terms depending on the gauge parameter are completely determined by the lower orders in accordance with the Landau-Khalatnikov-Fradkin transformation.