Conformal geometrodynamics: True degrees of freedom in a truly canonical structure
- School of Engineering and Physical Sciences, University of Aberdeen, King's College, Aberdeen AB24 3UE, Scotland (United Kingdom) and Rutherford Appleton Laboratory, CCLRC, Chilton, Didcot, Oxon OX11 0QX (United Kingdom)
The standard geometrodynamics is transformed into a theory of conformal geometrodynamics by extending the Arnowitt-Deser-Misner (ADM) phase space for canonical general relativity to that consisting of York's mean exterior curvature time, conformal three-metric and their momenta. Accordingly, an additional constraint is introduced, called the conformal constraint. In terms of the new canonical variables, a diffeomorphism constraint is derived from the original momentum constraint. The Hamiltonian constraint then takes a new form. It turns out to be the sum of an expression that previously appeared in the literature and extra terms quadratic in the conformal constraint. The complete set of the conformal, diffeomorphism and Hamiltonian constraints are shown to be of first class through the explicit construction of their Poisson brackets. The extended algebra of constraints has as subalgebras the Dirac algebra for the deformations and Lie algebra for the conformorphism transformations of the spatial hypersurface. This is followed by a discussion of potential implications of the presented theory on the Dirac constraint quantization of general relativity. An argument is made to support the use of the York time in formulating the unitary functional evolution of quantum gravity. Finally, the prospect of future work is briefly outlined.
- OSTI ID:
- 20709570
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 71, Issue 12; Other Information: DOI: 10.1103/PhysRevD.71.124026; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
Similar Records
Representations of spacetime diffeomorphisms. II. Canonical geometrodynamics
Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach