Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-12-30
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
44 pages, references are added, organization of material is slightly modified (additional section is introduced), more details
Scientific paper
Based on preliminary analysis of the Hamiltonian formulation of the first order Einstein-Cartan action (arXiv:0902.0856 [gr-qc] and arXiv:0907.1553 [gr-qc]) we derive the Darboux coordinates, which are a unique and uniform change of variables preserving equivalence with the original action in all spacetime dimensions higher than two. Considerable simplification of the Hamiltonian formulation using the Darboux coordinates, compared with direct analysis, is explicitly demonstrated. Even an incomplete Hamiltonian analysis in combination with known symmetries of the Einstein-Cartan action and the equivalence of Hamiltonian and Lagrangian formulations allows us to unambiguously conclude that the \textit{unique} \textit{gauge} invariances generated by the first class constraints of the Einstein-Cartan action and the corresponding Hamiltonian are \textit{translation and rotation in the tangent space}. Diffeomorphism invariance, though a manifest invariance of the action, is not generated by the first class constraints of the theory.
Kiriushcheva N.
Kuz'min S. V.
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