Abstract
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.
- Received 15 October 1990
DOI:https://doi.org/10.1103/PhysRevD.43.1212
©1991 American Physical Society