Simplifying the spectral analysis of the volume operator

Details Simplifying the spectral analysis of the volume operator Simplifying the spectral analysis of the volume operator

1997-06-13

arxiv.org/abs/gr-qc/9706038v1

Nucl.Phys. B500 (1997) 405-420

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, TeX, to be published in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(97)00334-9

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.

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