ON THE GUPTA-BLEULER QUANTIZATION OF THE HAMILTONIAN-SYSTEMS WITH ANOMALIES

The Gupta-Bleuler quantization method of QED can be generalized to can onically quantized constrained systems with quantum second-class const raints. Such constraints may originate either from the second-class co nstraints, already presented in the classical description of the theor y, or they may have their sources in quantum effects, in which case th e theory is called anomalous. In this paper, I present a detailed desc ription of how the Gupta-Bleuler ideas can be implemented in these cas es and I argue that there are in principle no inconsistencies in quant um anomalous theories. Having quantized the anomalous theories canonic ally, I derive the path integral formulation of such theories and show that some new terms are necessarily present in this formulation. As a n example, I show how the chiral Schwinger model can be quantized in t he original fermionic formulation with no reference to the bosonized v ersion used in the literature so far. (C) 1994 Academic Press, Inc.