THE VOLUME OPERATOR IN DISCRETIZED QUANTUM GRAVITY

Abstract

We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a well-defined scalar product in this approach permits us to make definite statements about the hermiticity of quantum operators. We find that the spectrum of the volume operator is discrete, but that the nature of its eigenstates differs from that found in an earlier continuum treatment.

15 pages, TeX, 3 figures (postscript, compressed and uu-encoded), May 95

References in corpus (2)

• Discreteness of area and volume in quantum gravity
• NON-PERTURBATIVE SOLUTIONS FOR LATTICE QUANTUM GRAVITY

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