Path Integrals, and Classical and Quantum Constraints

TL;DR

This paper discusses a projection operator method using coherent state path integrals to quantize constrained systems, effectively addressing normalization issues and second class constraints that challenge traditional Dirac procedures.

Contribution

It introduces a novel projection operator approach with coherent state path integrals for quantizing constrained systems, overcoming limitations of conventional methods.

Findings

Successfully implements a regularized quantum constraints approach

Addresses normalization issues in constrained quantization

Handles second class constraints effectively

Abstract

Systems with constraints pose problems when they are quantized. Moreover, the Dirac procedure of quantization prior to reduction is preferred. The projection operator method of quantization, which can be most conveniently described by coherent state path integrals, enables one to directly impose a regularized form of the quantum constraints. This procedure also overcomes conventional difficulties with normalization and second class constraints that invalidate conventional Dirac quantization procedures.