THE VOLUME OPERATOR IN DISCRETIZED QUANTUM GRAVITY

TL;DR

This paper studies the spectral properties of the volume operator in discretized quantum gravity, revealing a discrete spectrum and differing eigenstates from continuum models, thanks to a well-defined scalar product.

Contribution

It introduces a lattice discretization framework that clarifies the hermiticity and spectral characteristics of the volume operator in quantum gravity.

Findings

The volume operator has a discrete spectrum.

Eigenstates differ from continuum quantum gravity models.

A well-defined scalar product enables rigorous operator analysis.

Abstract

We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a well-defined scalar product in this approach permits us to make definite statements about the hermiticity of quantum operators. We find that the spectrum of the volume operator is discrete, but that the nature of its eigenstates differs from that found in an earlier continuum treatment.