Eigenvalues of the volume operator in loop quantum gravity

TL;DR

This paper introduces a straightforward method for calculating eigenvalues of the volume operator in loop quantum gravity and derives their asymptotic distribution at large spins, aiding statistical approaches in quantum gravity.

Contribution

It presents a new simple method for eigenvalue calculation and derives the asymptotic distribution of volume operator eigenvalues in the classical limit.

Findings

Derived the asymptotic distribution of eigenvalues for large spins

Provided a simple calculation method for volume operator eigenvalues

Results facilitate statistical analysis in quantum gravity

Abstract

We present a simple method to calculate certain sums of the eigenvalues of the volume operator in loop quantum gravity. We derive the asymptotic distribution of the eigenvalues in the classical limit of very large spins which turns out to be of a very simple form. The results can be useful for example in the statistical approach to quantum gravity.