BRS invariant stochastic quantization of Einstein gravity
Abstract
Stochastic quantization of gravity was studied 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 the sense that the FokkerPlanck Hamiltonian is the generator of the fictitious time translation. Then is was shown that there exists a nilpotent BRS symmetry in an enlarged phase space of the firstclass constrained systems. The phase space is spanned by the dynamical variables, their canonical conjugate momentum variables, FaddeevPopov ghost and antighost. The general BRS invariant formulation was applied to stochastic quantization of gravity which is described as a secondclass constrained system in terms of a pair of Langevin equations coupled with white noises. It is shown that the stochastic action of gravity includes explicitly the De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear sigmamodels.
 Publication:

Unknown
 Pub Date:
 November 1989
 Bibcode:
 1989bisq.book.....N
 Keywords:

 Formalism;
 Gravitation;
 Gravitational Fields;
 Hamiltonian Functions;
 Invariance;
 Stochastic Processes;
 Canonical Forms;
 FokkerPlanck Equation;
 Operators (Mathematics);
 Thermodynamics and Statistical Physics