Simplifying the spectral analysis of the volume operator
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.
- Publication:
-
Nuclear Physics B
- Pub Date:
- February 1997
- DOI:
- 10.1016/S0550-3213(97)00334-9
- arXiv:
- arXiv:gr-qc/9706038
- Bibcode:
- 1997NuPhB.500..405L
- Keywords:
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- General Relativity and Quantum Cosmology
- E-Print:
- 19 pages, TeX, to be published in Nucl. Phys. B