Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-01-31
The Icfai Univ. J. Physics, 2 (2009) issue 4
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
latex 2e, 11pt, 48 pages, 1 latex figure, discussion added
Scientific paper
We propose an unified approach to loop quantum gravity and Fedosov quantization of gravity following the geometry of double spacetime fibrations and their quantum deformations. There are considered pseudo-Riemannian manifolds enabled with 1) a nonholonomic 2+2 distribution defining a nonlinear connection (N-connection) structure and 2) an Arnowitt-Deser-Misner 3+1 decomposition. The Ashtekar-Barbero variables are generalized and adapted to the N-connection structure which allows us to write the general relativity theory equivalently in terms of Lagrange-Finsler variables and related canonical almost symplectic forms and connections. The Fedosov results are re-defined for gravitational gauge like connections and there are analyzed the conditions when the star product for deformation quantization is computed in terms of geometric objects in loop quantum gravity. We speculate on equivalence of quantum gravity theories with 3+1 and 2+2 splitting and quantum analogs of the Einstein equations.
No associations
LandOfFree
Loop Quantum Gravity in Ashtekar and Lagrange-Finsler Variables and Fedosov Quantization 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 Loop Quantum Gravity in Ashtekar and Lagrange-Finsler Variables and Fedosov Quantization of General Relativity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Loop Quantum Gravity in Ashtekar and Lagrange-Finsler Variables and Fedosov Quantization of General Relativity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-204894