Einstein gravity in almost Kahler and Lagrange-Finsler variables and deformation quantization

JOURNAL OF GEOMETRY AND PHYSICS

卷:60

Article

Vacaru, Sergiu I.

关键词: Einstein spaces;    Lagrange geometry;    Finsler geometry;    Deformation quantization;    Quantum gravity;   

DOI  :  10.1016/j.geomphys.2010.05.001

来源: Elsevier

【 摘 要 】

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 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 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. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free