Semiclassical path measure and factor ordering in quantum cosmology

Journal Article · Mon Feb 01 04:00:00 EST 1988 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(88)90170-4· OSTI ID:7111481

Louko, J

The euclidean path integral over compact four-metrics proposed by Hartle and Hawking to define the quantum state of the Universe is examined in the full semiclassical approximation Psi = P exp(-I/sup c/), where I/sup c/ is the action of the extremum and the prefactor P is given by a gaussian integral over small fluctuations around the extremum. We consider spatially homogeneous minisuperspace models of Bianchi types I and III and of the Kantowski--Sachs type, and infinite dimensional models containing the perturbative gravitational field and a massless scalar field on a k = +1 Friedmann--Robertson--Walker minisuperspace background. The prefactor is evaluated using zeta-function regularisation and adopting a scale invariant measure, and it is then related to the factor ordering dependent first derivative terms in the Wheeler--DeWitt equation H-italic-circumflexPsi = 0 through the semiclassical expansion. In the minisuperspace models, the prefactor obtained is consistent with ordering the kinetic term in H-italic-circumflex as the natural Laplacian as proposed by Hawking and Page. In the infinite dimensional models, a preferred factor ordering may be found by regularising the divergent semiclassical expansion of the Wheeler--DeWitt equation naively in terms of the Riemann zeta-function; however, no contact with covariant regularisation methods or an infinite dimensional Laplacian is attepted. copyright 1988 Academic Press, Inc.

• Research Organization: DAMTP, University of Cambridge, Silver Street, Cambridge CB3 9EW, England
• OSTI ID: 7111481
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 181:2; ISSN APNYA
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
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GRAND UNIFIED THEORY
INTEGRALS
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