Oneloop quantum cosmology: ζfunction technique for the HartleHawking wave function of the universe.
Abstract
The authors develop the oneloop calculational technique for the cosmological wave function in the noboundary proposal of Hartle and Hawking. This proposal is reformulated as a path integral over true physical variables in the unitary quantum gravity theory analytically continued from the Lorentzian spacetime to the compact Euclidean one. Then the oneloop calculation of this integral and its covariant renormalization reduce to the construction of the generalized ζfunctions for differential operators on the balllike Euclidean manifold. For ζfunctions of such operators with the explicitly unknown spectra the authors work out a special calculational algorithm based only on the knowledge of their basis functions and discuss in much detail their general properties in field theories as well as in quantum mechanical problems. This general technique is applied to the calculation of the oneloop graviton wave function of the de Sitter universe.
 Publication:

Annals of Physics
 Pub Date:
 November 1992
 DOI:
 10.1016/00034916(92)90347O
 Bibcode:
 1992AnPhy.219..201B