BRS Symmetry in Stochastic Quantization of Gravity

Abstract

A canonical formulation for stochastic quantization of gravity is proposed in the sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. The phase space is spanned by the original field variables, their canonical conjugate momenta which are introduced' artificially, Faddeev-Popov ghost and anti,ghost. Then we show that there exists a nilpotent BRS symmetry in the enlarged phase space. It is also shown that the stochastic action of gravity includes explicitly DeWitt's type metric in the configuration space which leads to a geometrical interpretation of quantum gravity analogous to nonlinear 6-models.