Canonical quantization of systems with time-dependent constraints

TL;DR

This paper discusses the Hamilton-Jacobi approach to quantizing systems with time-dependent constraints, deriving canonical coordinates without gauge fixing, and applying it to a relativistic particle in a plane wave, resulting in Klein-Gordon theory.

Contribution

It introduces a gauge-free method for canonical phase-space coordinate derivation and applies it to a relativistic particle, leading to a path integral formulation.

Findings

Canonical phase-space coordinates obtained without gauge fixing

Path integral quantization derived for the system

Resulting theory is equivalent to Klein-Gordon for a particle in a plane wave

Abstract

The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for the relativistic particle in a plane wave lead us to obtain the canonical phase-space coordinates with out using any gauge fixing condition. As a result of the quantization, we obtain the Klein-Gordon theory for a particle in a plane wave. The path integral quantization for this system is obtained using the canonical path integral formulation method.