Curing Fermion Mass Gauge Variance in QED$_{2+1}$
  The problem of the gauge dependence of the fermion mass in the Maxwell-Chern-Simons QED$_{2+1}$ is revisited. Using Proca mass term as an intermediate infrared regulator we are demonstrating gauge-invariance of the fermion mass shell in QED$_{2+1}$ in all orders of the perturbation theory. 
I.V.Tyutin and Vadim Zeitlin (Lebedev Phys. Inst.)