Simplifying the spectral analysis of the volume operator
General Relativity and Quantum Cosmology
2009-10-30 v1
Abstract
The volume operator plays a central role in both the kinematics and dynamics of canonical approaches to quantum gravity which are based on algebras of generalized Wilson loops. We introduce a method for simplifying its spectral analysis, for quantum states that can be realized on a cubic three-dimensional lattice. This involves a decomposition of Hilbert space into sectors transforming according to the irreducible representations of a subgroup of the cubic group. As an application, we determine the complete spectrum for a class of states with six-valent intersections.
Cite
@article{arxiv.gr-qc/9706038,
title = {Simplifying the spectral analysis of the volume operator},
author = {R. Loll},
journal= {arXiv preprint arXiv:gr-qc/9706038},
year = {2009}
}
Comments
19 pages, TeX, to be published in Nucl. Phys. B