Gauge-invariant chiral Schwinger model with Faddeevian regularization: Stuckelberg term, operator solution, and Hamiltonian and BRST formulations

Abstract

A chiral Schwinger model with the Faddeevian regularization a la Mitra is studied in one-space one-time dimension in the conventional form of dynamics (on the hyperplanes x0 = constant) called the “Instant-Form” (IF) dynamics. The original IF theory is seen to be gauge-noninvariant (GNI). Corresponding to this GNI model, a gauge-invariant (GI) theory is constructed through the so-called Stueckelberg term. The operator solution and the Hamiltonian and BRST formulations of the resulting GI theory, obtained by the inclusion of the Stueckelberg term in the action of the original GNI theory, are then investigated with some specific gauge choices. The physical contents of the original GNI theory are also recovered from the newly constructed GI theory under a special gauge.