Observability and Geometry in Three dimensional quantum gravity

TL;DR

This paper explores the coupling of particles with three-dimensional quantum gravity, constructing geometric operators as Dirac observables, and develops a loop quantum gravity quantization including a spin-foam model and distance operator.

Contribution

It introduces a novel approach to defining geometric operators in 3D quantum gravity coupled with particles using loop quantum gravity techniques.

Findings

Construction of a physical distance operator in 3D quantum gravity

Development of a spin-foam model for the coupled system

Quantization of geometric operators as Dirac observables

Abstract

We consider the coupling between massive and spinning particles and three dimensional gravity. This allows us to construct geometric operators (distances between particles) as Dirac observables. We quantize the system a la loop quantum gravity: we give a description of the kinematical Hilbert space and construct the associated spin-foam model. We construct the physical disctance operator and consider its quantization.