Simplifying the spectral analysis of the volume operator
نویسنده
چکیده
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. PACS: 04.60.Ds, 04.60.Nc, 02.20.Rt keywords: canonical quantum gravity, volume operator, lattice gravity, determinant of the metric, octagonal group * e-mail: [email protected]
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