Gauge invariance of (2+1)-dimensional QED

The problem of gauge invariance of the physical sector is studied in (2 + 1)-dimensional Maxwell-Chern-Simons QED (QED(2 + 1)). For the procedure employing the Proca mass term to perform infrared regularization, it is shown that the fermion mass is gauge-invariant and that the mass shell in QED(2 + 1) is well defined in all orders of perturbation theory. A class of gauges (including the transverse and Feynman gauges) that lead to the physical sector that is well defined and which is independent of the gauge parameter is indicated in QED(2 + 1).