On the Gupta-Bleuler Quantization of the Hamiltonian Systems with Anomalies

Abstract

The Gupta-Bleuler quantization method of QED can be generalized to canonically quantized constrained systems with quantum second-class constraints. Such constraints may originate either from the second-class constraints, already presented in the classical description of the theory, or they may have their sources in quantum effects, in which case the theory is called anomalous. In this paper, I present a detailed description of how the Gupta-Bleuler ideas can be implemented in these cases and I argue that there are in principle no inconsistencies in quantum anomalous theories. Having quantized the anomalous theories canonically, I derive the path integral formulation of such theories and show that some new terms are necessarily present in this formulation. As an example, I show how the chiral Schwinger model can be quantized in the original fermionic formulation with no reference to the bosonized version used in the literature so far.