BRS Symmetry in Stochastic Quantization of the Gravitational Field

Abstract

We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in a sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space for gravity (in general, for the first-class constrained systems). The stochastic action of gravity includes explicitly an unique DeWitt’s type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models.