The Stochastic Quantization of the Gravitational Field and the Gribov Problem

The stochastic quantization method proposed by Parisi and Wu is applied to the gravitational field. It is found that the Faddeev-Popov distribution for an arbitrary gauge condition, which is obtained in the conventional gauge theories, satisfies the modified equilibrium Fokker-Planck.equation by the proper choice of a parameter. It is also shown that the motion of a solution to the Langevin equation for the gravitational field is confined in a region (the Gribov region) where the Faddeev- Popov distribution is positive, if the solution is initially located inside the region. § 1. Introduction an