The Volume Operator in Spherically Symmetric Quantum Geometry

TL;DR

This paper computes the eigenstates and eigenvalues of the spherically symmetric volume operator in quantum geometry, revealing how its spectrum extends the homogeneous case with additional fine structure, aiding future physical studies.

Contribution

It provides a complete derivation of the spherically symmetric volume operator's spectrum, enhancing the explicit calculus for quantum models with spherical symmetry.

Findings

Spectrum related to homogeneous case with added fine structure

Eigenstates and eigenvalues explicitly computed

Facilitates future physical investigations in quantum gravity

Abstract

The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger spherically symmetric volume spectrum adds fine structure to the homogeneous spectrum. The formulas of this paper complete the derivation of an explicit calculus for spherically symmetric models which is needed for future physical investigations.