An SL(2,R) Model of Constrained Systems: Algebraic Constraint Quantization

TL;DR

This paper applies an algebraic constraint quantization scheme to an SL(2,R) gauge-invariant model, successfully identifying the physical representation of the algebra of observables and demonstrating a systematic approach to quantizing constrained systems.

Contribution

It introduces an algebraic constraint quantization method specifically for an SL(2,R) model with gauge symmetry, providing a clear procedure for identifying physical states.

Findings

Unambiguous identification of the physical representation of the algebra of observables.

Demonstration of the algebraic scheme's effectiveness in a gauge-invariant model.

Clarification of the role of algebraic constraints in quantization.

Abstract

A reparametrization invariant model, introduced by Montesinos, Rovelli and Thiemann, possessing an SL(2,R) gauge symmetry is treated along the guidelines of an algebraic constraint quantization scheme that translates the vanishing of the constraints into representation conditions for the algebra of observables. The application of this algebraic scheme to the SL(2,R) model yields an unambiguous identification of the physical representation of the algebra of observables.