Geometrical measurements in three-dimensional quantum gravity

TL;DR

This paper introduces a set of geometrically interpretable observables for 3D quantum gravity, linking spin network evaluations to measurable distances in a topological quantum field theory.

Contribution

It presents a novel framework for measuring distances in 3D quantum gravity using spin networks and Fourier transforms, with clear geometrical interpretations.

Findings

Spectra and probabilities with geometric meaning

Observables related to relativistic spin networks

Framework applicable to positive cosmological constant

Abstract

A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the distances between points, giving spectra and probabilities which have a geometrical interpretation. The observables are related to the evaluation of relativistic spin networks by a Fourier transform.