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 Fokker-Planck 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 first-class constrained systems. The phase space is spanned by the dynamical variables, their canonical conjugate momentum variables, Faddeev-Popov ghost and anti-ghost. The general BRS invariant formulation was applied to stochastic quantization of gravity which is described as a second-class 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 sigma-models.
- Publication:
-
Unknown
- Pub Date:
- November 1989
- Bibcode:
- 1989bisq.book.....N
- Keywords:
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- Formalism;
- Gravitation;
- Gravitational Fields;
- Hamiltonian Functions;
- Invariance;
- Stochastic Processes;
- Canonical Forms;
- Fokker-Planck Equation;
- Operators (Mathematics);
- Thermodynamics and Statistical Physics