Observables in 3-dimensional quantum gravity and topological invariants

TL;DR

This paper explores the expectation values of specific observables in 3D Riemannian quantum gravity with positive cosmological constant, using examples to illustrate a topological computation method within the Turaev-Viro model.

Contribution

It provides a practical approach to compute expectation values of observables in the Turaev-Viro model through examples, highlighting a topological procedure.

Findings

Expectation values can be computed via topological methods.

Examples demonstrate the applicability of the approach.

Provides a framework for understanding observables in 3D quantum gravity.

Abstract

In this paper we report some results on the expectation values of a set of observables introduced for 3-dimensional Riemannian quantum gravity with positive cosmological constant, that is, observables in the Turaev-Viro model. Instead of giving a formal description of the observables, we just formulate the paper by examples. This means that we just show how an idea works with particular cases and give a way to compute 'expectation values' in general by a topological procedure.