Semiclassical Analysis of Constrained Quantum Systems

TL;DR

This paper presents an effective semiclassical method for analyzing constrained quantum systems, simplifying the Dirac quantization process by avoiding complex representations and illustrating it with a relativistic particle example.

Contribution

It introduces a geometrically motivated semiclassical scheme that approximates constrained quantum dynamics without relying on specific Hilbert space representations.

Findings

Provides a practical semiclassical correction scheme for gauge theories

Avoids complex Hilbert space constructions in constrained quantization

Demonstrates the method with a relativistic particle example

Abstract

Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical corrections to the dynamics of constrained quantum systems developed elsewhere. Motivated by the geometrical view of quantum mechanics, our method mimics the classical Dirac-Bergmann algorithm and avoids direct reference to a particular representation of the physical Hilbert space. We illustrate the procedure through the example of a relativistic particle in Minkowski spacetime.