Rdeduced phase-space quantization of constrained systems

TL;DR

This paper explores a Hamilton-Jacobi approach to constrained systems, deriving reduced phase-space coordinates without gauge fixing, and discusses operator and path integral quantization methods.

Contribution

It introduces a gauge-free method for obtaining reduced phase-space coordinates in constrained systems using Hamilton-Jacobi equations.

Findings

Derived equations of motion as total differentials in many variables.

Established integrability conditions leading to canonical reduced phase-space.

Discussed operator and path integral quantization approaches.

Abstract

The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion for three singular systems are obtained as total differential equations in many variables. The integrability conditions for these syatems lead us to the canonical reduced phase-space coordinates with out using any gauge fixing conditions. The operator and the path integral quantization of these systems is discussed.