Geometrodynamics regained: A Lagrangian approach
- 1 June 1974
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 15 (6) , 708-715
- https://doi.org/10.1063/1.1666715
Abstract
The closing relation between two super-Hamiltonians is cast into a condition on the super-Lagrangian by a functional Legendre transformation. It is shown that the ADM super-Lagrangian provides the unique representation of the ``group'' of deformations of a spacelike hypersurface embedded in a Riemannian space-time when the intrinsic geometry gij of the hypersurface is allowed as the sole configuration variable. No such uniqueness exists for the super-Lagrangians of source fields. As an illustration, the most general super-Lagrangian for a scalar field with nonderivative gravitational coupling is recovered from the closing relation.Keywords
This publication has 7 references indexed in Scilit:
- Mapping onto Solutions of the Gravitational Initial Value ProblemJournal of Mathematical Physics, 1972
- Gravitational Degrees of Freedom and the Initial-Value ProblemPhysical Review Letters, 1971
- The Einstein Tensor and Its GeneralizationsJournal of Mathematical Physics, 1971
- Quantum Theory of Gravity. I. The Canonical TheoryPhysical Review B, 1967
- Integration of Secondary Constraints in Quantized General RelativityPhysical Review Letters, 1959
- Integration of Secondary Constraints in Quantized General RelativityPhysical Review Letters, 1958
- Feynman Quantization of General RelativityReviews of Modern Physics, 1957