Spectral Analysis of the Volume Operator in Loop Quantum Gravity

Abstract

We describe preliminary results of a detailed numerical analysis of the volume operator as formulated by Ashtekar and Lewandowski. Due to a simplified explicit expression for its matrix elements, it is possible for the first time to treat generic vertices of valence greater than four. It is found that the vertex geometry characterizes the volume spectrum.

5 pages, 1 figure. Talk given by D. Rideout at the Eleventh Marcel Grossmann Meeting on General Relativity at the Freie U. Berlin, July 23 - 29, 2006

References in corpus (1)

• Spectral Analysis of the Volume Operator in Loop Quantum Gravity

Cited by in corpus (16)

• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Loop Quantum Gravity: An Inside View
• Spectral Analysis of the Volume Operator in Loop Quantum Gravity
• The length operator in Loop Quantum Gravity
• Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?
• Consistent Loop Quantum Cosmology
• Loop and spin foam quantum gravity: a brief guide for beginners
• Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
• The Volume Operator in Spherically Symmetric Quantum Geometry
• A semiclassical tetrahedron
• Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States
• Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model
• On Loop States in Loop Quantum Gravity
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology
• Three-geometry and reformulation of the Wheeler-DeWitt equation