Quantum gravitational measure for three-geometries

Details Quantum gravitational measure for three-geometries Quantum gravitational measure for three-geometries

1997-01-09

arxiv.org/abs/hep-th/9701033v1

Phys.Lett. B262 (1991) 405-410

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, TeX. This is the original, preprint version of the paper that with some modifications was published in

Scientific paper

10.1016/0370-2693(91)90613-U

The gravitational measure on an arbitrary topological three-manifold is constructed. The nontrivial dependence of the measure on the conformal factor is discussed. We show that only in the case of a compact manifold with boundary the measure acquires a nontrivial dependence on the conformal factor which is given by the Liouville action. A nontrivial Jacobian (the divergent part of it) generates the Einstein-Hilbert action. The Hartle-Hawking wave function of Universe is given in terms of the Liouville action. In the gaussian approximation to the Wheeler-DeWitt equation this result was earlier derived by Banks et al. Possible connection with the Chern-Simons gravity is also discussed.

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