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.

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

References in corpus (4)

• Further results on geometric operators in quantum gravity
• Imposing det E > 0 in discrete quantum gravity
• Latticing quantum gravity
• Still on the way to quantizing gravity

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• Loop Quantum Cosmology II: Volume Operators
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