PIRSA:08020041

Loop Quantum Gravity and Deformation Quantization

Vacaru, S. (2008). Loop Quantum Gravity and Deformation Quantization. Perimeter Institute. https://pirsa.org/08020041

Vacaru, Sergiu. Loop Quantum Gravity and Deformation Quantization. Perimeter Institute, Feb. 07, 2008, https://pirsa.org/08020041 

          @misc{ pirsa_PIRSA:08020041,
            doi = {10.48660/08020041},
            url = {https://pirsa.org/08020041},
            author = {Vacaru, Sergiu},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Loop Quantum Gravity and Deformation Quantization},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {feb},
            note = {PIRSA:08020041 see, \url{https://pirsa.org}}
          }

Sergiu Vacaru

University of Toronto

Talk number
PIRSA:08020041
Collection
Talk Type
Subject
Abstract
Loop Quantum Gravity and Deformation Quantization Abstract: We propose a 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 ADM 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.