Eigenvalues of the volume operator in loop 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.

12 pages, version accepted in Class. Quantum Grav

References in corpus (10)

• Background Independent Quantum Gravity: A Status Report
• Discreteness of area and volume in quantum gravity
• Quantum Geometry and Black Hole Entropy
• Black hole entropy in Loop Quantum Gravity
• Black hole entropy from Quantum Geometry
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• Closed formula for the matrix elements of the volume operator in canonical quantum gravity
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Cited by in corpus (12)

• Discreteness of the volume of space from Bohr-Sommerfeld quantization
• Properties of the Volume Operator in Loop Quantum Gravity I: Results
• Bohr-Sommerfeld Quantization of Space
• Deformations of Polyhedra and Polygons by the Unitary Group
• Properties of the Volume Operator in Loop Quantum Gravity II: Detailed Presentation
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Turning big bang into big bounce: II. Quantum dynamics
• Hamiltonian dynamics of a quantum of space: hidden symmetries and spectrum of the volume operator, and discrete orthogonal polynomials
• The Large-Volume Limit of a Quantum Tetrahedron is a Quantum Harmonic Oscillator
• Three-geometry and reformulation of the Wheeler-DeWitt equation
• Classical and Quantum Polyhedra
• Categorical Quantum Volume Operator