General covariance of the path integral for quantum gravity

Bern, Zvi; Mottola, Emil; Blau, Steven K.

doi:10.1103/PhysRevD.43.1212

General covariance of the path integral for quantum gravity

Oct 15, 1990

23 pages

Published in:

Phys.Rev.D 43 (1991) 1212-1222

DOI:

10.1103/PhysRevD.43.1212

Report number:

LA-UR-90-3172

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Abstract: (APS)

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.

quantum gravity
path integral
invariance: Lorentz
gauge field theory: Yang-Mills
invariance: Becchi-Rouet-Stora
ghost
background field
differential geometry

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