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Simplifying the spectral analysis of the volume operator | | R. Loll
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13 Jun 1997 | | Journal: | Nucl.Phys. B500 (1997) 405-420 | | Subject: | gr-qc | | Affiliation: | AEI, Potsdam | | 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. | | Source: | arXiv, gr-qc/9706038 | | Services: | Forum | Review | PDF | Favorites | |
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