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Simplifying the spectral analysis of the volume operator

R. Loll
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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.

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R. Loll. 1997-06-13. Simplifying the spectral analysis of the volume operator. https://doi.org/10.1016/s0550-3213(97)00334-9

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