Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles

Understand

We provide a method of converting Lagrange and Finsler spaces and their Legendre transforms to Hamilton and Cartan spaces into almost Kaehler 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 deformation quantization schemes for nonlinear mechanical and gravity models on Lagrange- and Hamilton-Fedosov manifolds.