Einstein Gravity as a Nonholonomic Almost Kahler Geometry,
Lagrange-Finsler Variables, and Deformation Quantization
release_xijsootlx5finipwa6e6je3zqu
by
Sergiu I. Vacaru
2010
Abstract
A geometric procedure is elaborated for transforming (pseudo) Riemanian
metrics and connections into canonical geometric objects (metric and nonlinear
and linear connections) for effective Lagrange, or Finsler, geometries which,
in their turn, can be equivalently represented as almost Kahler spaces. This
allows us to formulate an approach to quantum gravity following standard
methods of deformation quantization. Such constructions are performed not on
tangent bundles, as in usual Finsler geometry, but on spacetimes enabled with
nonholonomic distributions defining 2+2 splitting with associate nonlinear
connection structure. We also show how the Einstein equations can be redefined
in terms of Lagrange-Finsler variables and corresponding almost symplectic
structures and encoded into the zero-degree cohomology coefficient for a
quantum model of Einstein manifolds.
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