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The volume operator in spherically symmetric quantum geometry

Martin Bojowald and Rafal Swiderski

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The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analogue, the spectra are related in the sense that the larger spherically symmetric volume spectrum adds fine structure to the homogeneous spectrum. The formulae of this paper complete the derivation of an explicit calculus for spherically symmetric models which is needed for future physical investigations.


PACS

04.60.Pp Loop quantum gravity, quantum geometry, spin foams

02.10.Ud Linear algebra

02.30.Tb Operator theory

MSC

15A18 Eigenvalues, singular values, and eigenvectors

83Cxx General relativity

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 21 (7 November 2004)

Received 15 July 2004

Published 7 October 2004



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