Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-07-09
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
48 pages
Scientific paper
The Hamiltonian formulation of N-bein, Einstein-Cartan, gravity, using its first order form in any dimension higher than two, is analyzed. This Hamiltonian formulation allows to explicitly show where peculiarities of three dimensional case (\textit{A.M.Frolov et al, 0902.0856 [gr-qc]}) occur and make a conjecture, based on presented in this report results, that there is one general for \textit{all} dimensions characteristic of N-bein formulation of gravity: after elimination of second class constraints the algebra of Poisson brackets among remaining first class secondary constraints is the Poincare algebra and in all dimensions N-bein, Cartan-Einstein, gravity \textit{is the Poincare gauge theory}. The gauge symmetry corresponding to the algebra of first class constraints has two parameters - rotational (Lorentz) and translational. Translational invariance is common to all dimensions but some terms in general expressions for gauge transformations of N-beins and connections are zero in a particular, three dimensional, case. The proof of our conjecture is outlined in detail. Some straightforward but tedious calculations remain to be completed to call our conjecture - a theorem and will be reported later.
Kiriushcheva N.
Kuz'min S. V.
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