Bohr-Sommerfeld Quantization of Space

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.

32 pages, 10 figures

References in corpus (5)

• Polyhedra in loop quantum gravity
• From twistors to twisted geometries
• Spectral Analysis of the Volume Operator in Loop Quantum Gravity
• Zakopane lectures on loop gravity
• Discreteness of the volume of space from Bohr-Sommerfeld quantization

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