Path integral for gravity and supergravity

It is shown that the specification of the path integral variables in quantum gravity, which was previously formulated on the basis of the anomaly consideration and the BRS supersymmetry, can also be understood by the more familiar consideration of the unit jacobian approach. We describe how to derive the same prescription in the framework of the basic path integral formalism without recourse to the BRS supersymmetry, which is one of the consequences of the Faddeev-Popov effective action. A novel feature of quantum gravity (and the gauge theory in curved space-time in general) is that a proper choice of the invariant gauge orbit volume element becomes essential to ensure the gauge independence of the partition function. We also briefly note that the conformal (Weyl) symmetry is generally spoiled by the anomaly in quantum theory. The connection between the present 'anomaly-free' prescription and the true gravitational anomaly by Alvarez-Gaume and Witten is also clarified. (orig.)