New Measures for the Quantization of Systems with Constraints

TL;DR

This paper introduces new quantization methods for constrained systems, focusing on phase-space path integration, reparameterization invariance, and spectral gap considerations, enhancing the theoretical framework for such systems.

Contribution

It extends the formalism of quantization for systems with constraints by providing new examples and addressing cases with spectral gaps in the operator form of constraints.

Findings

New quantization examples for reparameterization invariant Hamiltonians

Extension of formalism to include spectral gap cases

Enhanced understanding of phase-space path integration in constrained systems

Abstract

Based on the results of a recent reexamination of the quantization of systems with first-class and second-class constraints from the point of view of coherent-state phase-space path integration, we give additional examples of the quantization procedure for reparameterization invariant Hamiltonians, for systems for which the original set of Lagrange multipliers are elevated to dynamical variables, as well as extend the formalism to include cases of first-class constraints the operator form of which have a spectral gap about the value zero that characterizes the quantum constraint subspace.