Bohr-Sommerfeld Quantization of Space

TL;DR

This paper applies semiclassical Bohr-Sommerfeld quantization to the classical tetrahedral volume in loop gravity, revealing insights into the volume spectrum and its degeneracies, with results matching quantum computations.

Contribution

It introduces a semiclassical approach to analyze the volume spectrum in loop gravity, providing new geometric understanding and quantitative agreement with quantum results.

Findings

Quantitative agreement with loop gravity volume spectrum

Insights into degeneracy and eigenvalues of volume

Semiclassical methods elucidate geometric structure

Abstract

We introduce semiclassical methods into the study of the volume spectrum in loop gravity. The classical system behind a 4-valent spinnetwork node is a Euclidean tetrahedron. We investigate the tetrahedral volume dynamics on phase space and apply Bohr-Sommerfeld quantization to find the volume spectrum. The analysis shows a remarkable quantitative agreement with the volume spectrum computed in loop gravity. Moreover, it provides new geometrical insights into the degeneracy of this spectrum and the maximum and minimum eigenvalues of the volume on intertwiner space.