Properties of the Volume Operator in Loop Quantum Gravity II: Detailed Presentation

Details Properties of the Volume Operator in Loop Quantum Gravity II: Detailed Presentation Properties of the Volume Operator in Loop Quantum Gravity II: Detailed Presentation

2007-06-04

arxiv.org/abs/0706.0382v2

Class.Quant.Grav.25:065002,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Companion to arXiv:0706.0469. Version as published in CQG in 2008. More compact presentation. Sign factor combinatorics now mu

Scientific paper

10.1088/0264-9381/25/6/065002

The properties of the Volume operator in Loop Quantum Gravity, as constructed by Ashtekar and Lewandowski, are analyzed for the first time at generic vertices of valence greater than four. The present analysis benefits from the general simplified formula for matrix elements of the Volume operator derived in gr-qc/0405060, making it feasible to implement it on a computer as a matrix which is then diagonalized numerically. The resulting eigenvalues serve as a database to investigate the spectral properties of the volume operator. Analytical results on the spectrum at 4-valent vertices are included. This is a companion paper to arXiv:0706.0469, providing details of the analysis presented there.

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