Geometric quantization of relativistic Hamiltonian mechanics

TL;DR

This paper develops a geometric quantization framework for relativistic Hamiltonian systems modeled as Dirac constraint systems, leading to a relativistic quantum equation.

Contribution

It introduces a geometric quantization approach for relativistic Hamiltonian mechanics viewed as a Dirac constraint system.

Findings

Quantization of the cotangent bundle yields a relativistic quantum equation.

Framework connects classical relativistic mechanics with quantum theory.

Provides geometric tools for quantizing constrained relativistic systems.

Abstract

A relativistic Hamiltonian mechanical system is seen as a conservative Dirac constraint system on the cotangent bundle of a pseudo-Riemannian manifold. We provide geometric quantization of this cotangent bundle where the quantum constraint serves as a relativistic quantum equation.