Generalized Lagrange Transforms: Finsler Geometry Methods and Deformation Quantization of Gravity

Details Generalized Lagrange Transforms: Finsler Geometry Methods and Deformation Quantization of Gravity Generalized Lagrange Transforms: Finsler Geometry Methods and Deformation Quantization of Gravity

2007-07-11

arxiv.org/abs/0707.1526v2

, An. St. Univ. Al. I. Cuza din Iasi (S.N.), Matematica, vol LIII, 2007, Supliment, 327-342

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

latex 2e, 11pt, 17 pages, to be published: An. St. Univ. Al. I. Cuza, Iasi, s I a, Matematica, vol LIII (suplement), 2007

Scientific paper

We propose a natural Fedosov type quantization of generalized Lagrange models and gravity theories with metrics lifted on tangent bundle, or extended to higher dimension, following some stated geometric/ physical conditions (for instance, nonholonomic and/or conformal transforms to some physically important metrics or mapping into a gauge model). Such generalized Lagrange transforms define canonical nonlinear connection, metric and linear connection structures and model almost Kahler geometries with induced canonical symplectic structure and compatible affine connection. The constructions are possible due to a synthesis of the nonlinear connection formalism developed in Finsler and Lagrange geometries and deformation quantization methods.

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