Geometrodynamics regained: A Lagrangian approach
- 1 June 1974
- journal article
- research 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
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