Deformation Quantization of Nonholonomic Almost Kähler Models and Einstein Gravity
نویسنده
چکیده
Nonholonomic distributions and adapted frame structures on (pseudo) Riemannian manifolds of even dimension are employed to build structures equivalent to almost Kähler geometry and which allows to perform a Fedosov-like quantization of gravity. The nonlinear connection formalism that was formally elaborated for Lagrange and Finsler geometry is implemented in classical and quantum Einstein gravity.
منابع مشابه
Branes and Quantization for an A–Model Complexification of Einstein Gravity in Almost Kähler Variables
The general relativity theory is redefined equivalently in almost Kähler variables: symplectic form, θ[g], and canonical symplectic connection, D̂[g] (distorted from the Levi–Civita connection by a tensor constructed only from metric coefficients and their derivatives). The fundamental geometric and physical objects are uniquely determined in metric compatible form by a (pseudo) Riemannian metri...
متن کاملFedosov Quantization of Lagrange–Finsler and Hamilton–Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
We provide a method of converting Lagrange and Finsler spaces and their Legendre transforms to Hamilton and Cartan spaces into almost Kähler structures on tangent and cotangent bundles. In particular cases, the Hamilton spaces contain nonholonomic lifts of (pseudo) Riemannian / Einstein metrics on effective phase spaces. This allows us to define the corresponding Fedosov operators and develop d...
متن کاملEinstein Gravity in Almost Kähler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics
We argue that the Einstein gravity theory can be reformulated in almost Kähler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation (NGT) on manifolds enabled with nonholonomic distributions is analyzed. There are considered some conditions when the fundamental g...
متن کاملEinstein Gravity as a Nonholonomic Almost Kähler Geometry, Lagrange–finsler Variables, and Deformation Quantization
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 Kähler spaces. This allows us to formulate an approach to quantum gravity following standard methods of deforma...
متن کاملGravity as a Nonholonomic Almost Kähler
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 Kähler spaces. This allows us to formulate an approach to quantum gravity following standard methods of deforma...
متن کامل