Almost Kaehler deformation quantization
@article{Karabegov2001AlmostKD, title={Almost Kaehler deformation quantization}, author={Alexander Karabegov and Martin Schlichenmaier}, journal={arXiv: Quantum Algebra}, year={2001} }
We use a natural affine connection with nontrivial torsion on an arbitrary almost-Kaehler manifold which respects the almost-Kaehler structure to construct a Fedosov-type deformation quantization on this manifold.
3 Citations
Three Natural Generalizations of Fedosov Quantization
- Mathematics
- 2009
Fedosov's simple geometrical construction for deformation quantization of sym- plectic manifolds is generalized in three ways without introducing new variables: (1) The base manifold is allowed to be…
Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance
- Mathematics
- 2001
Gromov-Hausdorff distance for quantum metric spaces Bibliography Matrix algebras Converge to the sphere for quantum Gromov-Hausdorff distance Bibliography.
On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles
- Physics
- 2018
We develop an axiomatic geometric approach and provide an unconventional review of modified gravity theories, MGTs, with modified dispersion relations, MDRs, encoding Lorentz invariance violations,…
36 References
Pseudo-Kähler Quantization on Flag Manifolds
- Mathematics
- 1997
Abstract:A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kähler structure is proposed. In particular cases we…
Cohomological Classification of Deformation Quantizations with Separation of Variables
- Mathematics
- 1998
We calculate a second cohomology class which determines a deformation quantization up to equivalence for a deformation quantization with separation of variables on a Kähler manifold, following P.…
Quantization of Kähler manifolds. IV
- Mathematics
- 1994
We use Berezin's dequantization procedure to define a formal *-product on the algebra of smooth functions on the bounded symmetric domains. We prove that this formal *-product is convergent on a…
Quantization of Kähler manifolds II
- Mathematics
- 1993
We use Berezin’s dequantization procedure to define a formal *- product on a dense subalgebra of the algebra ofsmooth functions on a compact homogeneous Kahler manifold M. We prove that this formal…
Quantization of Kähler manifolds. III
- Mathematics
- 1994
We use Berezin's dequantization procedure to define a formal *-product on the algebra of smooth functions on the unit disk in ℂ. We prove that this formal *-product is convergent on a dense…
*-Products on some Kähler manifolds
- Mathematics
- 1986
Starting from work of F. A. Berezin, in this Letter we define an invariant *-product on every nonexceptional Kähler symmetric space. We then obtain a recursion formula to calculate the corresponding…
Deformation quantizations with separation of variables on a Kähler manifold
- Mathematics
- 1996
We give a simple geometric description of all formal differentiable deformation quantizations on a Kähler manifoldM such that for each open subsetU⊂M ⋆-multiplication from the left by a holomorphic…
Berezin-Toeplitz quantization of compact Kähler manifolds
- Mathematics
- 1996
In this lecture results are reviewed obtained by the author together with Martin Bordemann and Eckhard Meinrenken on the Berezin-Toeplitz quantization of compact Kaehler manifolds. Using global…
Deformation quantization of compact Kahler manifolds by Berezin-Toeplitz quantization
- Mathematics
- 1999
For arbitrary compact quantizable Kahler manifolds it is shown how a natural formal deformation quantization (star product) can be obtained via Berezin-Toeplitz operators. Results on their…