Conformal Foliations and Constraint Quantization

TL;DR

This paper explores how the classical constraint algebra of a parametrized relativistic gauge system induces a conformal foliation, which then guides the factor ordering in its canonical quantum operator formulation.

Contribution

It introduces a novel geometric approach using conformal foliations to determine factor ordering in the quantization of gauge systems.

Findings

Constraint algebra induces conformal foliation

Conformal foliations inform factor ordering in quantization

Provides a geometric framework for quantum operator ordering

Abstract

We show that the Classical Constraint Algebra of a Parametrized Relativistic Gauge System induces a natural structure of Conformal Foliation on a Transversal Gauge. Using the theory of Conformal Foliations, we provide a natural Factor Ordering for the Quantum Operators associated to the Canonical Quantization of such Gauge System.