A simple quantum-mechanical analogue of Siegel's action for chiral bosons

Abstract

A simple mechanical analogue of Siegel's action for chiral bosons is analyzed in the hope that it may shed some light on the controversy about the quantization of Siegel's action. At the classical level, the model has a gauge symmetry which becomes anomalous upon quantization. The model, however, can still be consistently quantized either by imposing the constraints weakly as in the covariant quantization of strings, or by treating the first-class constraints of the classical hamiltonian formalism as functions of two second-class constraints.