On Quantization of Time-Dependent Systems with Constraints

TL;DR

This paper addresses the challenge of quantizing time-dependent constrained systems by proposing a new derivation method based on an equivalent theory with no explicit time dependence.

Contribution

It introduces an independent approach to derive quantization rules for time-dependent constrained systems, expanding on existing methods.

Findings

New derivation method for quantization rules

Applicable to systems with explicit time-dependent constraints

Provides a consistent framework for such quantization

Abstract

The Dirac method of canonical quantization of theories with second class constraints has to be modified if the constraints depend on time explicitly. A solution of the problem was given by Gitman and Tyutin. In the present work we propose an independent way to derive the rules of quantization for these systems, starting from physical equivalent theory with trivial non-stationarity.