Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-12-17
Eur.Phys.J.C70:389-422,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
74 pages
Scientific paper
10.1140/epjc/s10052-010-1458-4
It is shown that the Hamiltonian of the Einstein affine-metric (first order) formulation of General Relativity (GR) leads to a constraint structure that allows the restoration of its unique gauge invariance, four-diffeomorphism, without the need of any field dependent redefinition of gauge parameters as is the case for the second order formulation. In the second order formulation of ADM gravity the need for such a redefinition is the result of the non-canonical change of variables [arXiv: 0809.0097]. For the first order formulation, the necessity of such a redefinition "to correspond to diffeomorphism invariance" (reported by Ghalati [arXiv: 0901.3344]) is just an artifact of using the Henneaux-Teitelboim-Zanelli ansatz [Nucl. Phys. B 332 (1990) 169], which is sensitive to the choice of linear combination of tertiary constraints. This ansatz cannot be used as an algorithm for finding a gauge invariance, which is a unique property of a physical system, and it should not be affected by different choices of linear combinations of non-primary first class constraints. The algorithm of Castellani [Ann. Phys. 143 (1982) 357] is free from such a deficiency and it leads directly to four-diffeomorphism invariance for first, as well as for second order Hamiltonian formulations of GR. The distinct role of primary first class constraints, the effect of considering different linear combinations of constraints, the canonical transformations of phase-space variables, and their interplay are discussed in some detail for Hamiltonians of the second and first order formulations of metric GR. The first order formulation of Einstein-Cartan theory, which is the classical background of Loop Quantum Gravity, is also discussed.
Kiriushcheva N.
Kuz'min S. V.
No associations
LandOfFree
The Hamiltonian of Einstein affine-metric formulation of General Relativity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Hamiltonian of Einstein affine-metric formulation of General Relativity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Hamiltonian of Einstein affine-metric formulation of General Relativity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-685734