کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1894968 | 1044260 | 2010 | 17 صفحه PDF | دانلود رایگان |
A geometric procedure is elaborated for transforming (pseudo) Riemannian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in turn, can be equivalently represented as almost Kähler 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+22+2 splitting with associate nonlinear connection structure. We also show how the Einstein equations can be written 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.
Journal: Journal of Geometry and Physics - Volume 60, Issue 10, October 2010, Pages 1289–1305