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Phys. Rev. D 43, 1212–1222 (1991)

General covariance of the path integral for quantum gravity

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Zvi Bern*, Steven K. Blau†, and Emil Mottola
Theoretical Division, T-8, Mail Stop B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

Received 15 October 1990; published in the issue dated 15 February 1991

We construct the functional integration measure over four-geometries in the path integral for quantum gravity by means of a geometric, manifestly covariant approach, similar to that used by Polyakov for string theory. This generalizes the previous one-loop method of Mazur and Mottola to all orders of perturbation theory. We compare this measure to that obtained by the gauge-fixed method of Becchi-Rouet-Stora-Tyutin invariance exploited by Fujikawa and co-workers. The path integral defined by these two different procedures is one and the same.

© 1991 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevD.43.1212
DOI:
10.1103/PhysRevD.43.1212
PACS:

*Present address: Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260.

†Present address: Physics Department, Amherst College, Amherst, MA 01002.

 
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