Coordinate-free quantization of first-class constrained systems

TL;DR

This paper develops a coordinate-free approach to quantizing constrained systems, including gauge theories, using path integrals, coherent states, and projection operators to handle gauge invariance.

Contribution

It extends the coordinate-free quantization method to a broad class of first-class constrained systems, including Yang-Mills theories, with a novel use of coherent states and Lagrange multipliers.

Findings

Successful extension of coordinate-free quantization to gauge theories

Implementation of projection operators for gauge invariance

Framework applicable to a wide class of constrained systems

Abstract

The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough to include Yang-Mills type theories with an arbitrary compact gauge group. Central to this extension are the use of coherent state path integrals and of Lagrange multiplier integrations that engender projection operators onto the subspace of gauge invariant states.