publication . Article . Preprint . 2013

deformation quantization with separation of variables of an endomorphism bundle

Karabegov, Alexander;
Open Access
  • Published: 26 Jul 2013 Journal: Journal of Geometry and Physics, volume 75, pages 55-70 (issn: 0393-0440, Copyright policy)
  • Publisher: Elsevier BV
Abstract
Comment: 29 pages, an important reference is added, several typos corrected
Subjects
arXiv: Mathematics::Symplectic GeometryMathematics::Differential GeometryAstrophysics::Galaxy AstrophysicsAstrophysics::Solar and Stellar AstrophysicsAstrophysics::Earth and Planetary Astrophysics
free text keywords: Mathematical Physics, General Physics and Astronomy, Geometry and Topology, Vector-valued differential form, Frame bundle, Mathematics, Topology, Dual bundle, Principal bundle, Connection (principal bundle), Tautological line bundle, Mathematical analysis, Clifford bundle, Normal bundle, Mathematics - Quantum Algebra, 53D55, 81T18
Related Organizations
29 references, page 1 of 2

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[3] Alekseev, A., Lachowska, A.: Invariant ∗-products on coadjoint orbits and the Shapovalov pairing. Comment. Math. Helv. 80 (2005), 795-810.

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[5] Berezin, F.A.: Quantization in complex symmetric spaces. Math. USSR-Izv. 39 (1975), 363-402. [OpenAIRE]

[6] Bordemann, M., Brischle, M., Emmrich, C., and Waldmann, S.: Phase space reduction for star-products: An explicit construction for Pn. Lett. Math. Phys. 36, (4)(1996), 357-371.

[7] Bordemann, M., Waldmann, S.: A Fedosov star product of the Wick type for K¨ahler manifolds. Lett. Math. Phys. 41 (3) (1997), 243 - 253.

[8] Engliˇs, M.: Weighted Bergman kernels and quantization, Commun. Math. Phys. 227 (2002), 211-241.

[9] Fedosov, B.: A simple geometrical construction of deformation quantization. J. Differential Geom. 40 (1994), no. 2, 213-238. [OpenAIRE]

[10] Fedosov, B.: Deformation quantization and index theory. Mathematical Topics. Vol. 9. Akademie Verlag, Berlin (1996).

[11] Gammelgaard, N. L.: A Universal Formula for Deformation Quantization on K¨ahler Manifolds, arXiv:1005.2094v2.

[12] Gutkin, E.: Overcomplete subspace systems and operator symbols. Func. Anal. Appl. 9 (1975) 260 - 262.

[13] Gutt, S. and Rawnsley, J.: Natural star products on symplectic manifolds and quantum moment maps. Lett. Math. Phys. 66 (2003), 123 -139. [OpenAIRE]

[14] Karabegov, A.: Operator-valued pq-symbols and geometric quantization. Func. Anal. and Appl. 29 (1995) 133-135.

[15] Karabegov, A.: Deformation quantizations with separation of variables on a K¨ahler manifold. Commun. Math. Phys. 180 (1996), no. 3, 745-755. [OpenAIRE]

29 references, page 1 of 2
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publication . Article . Preprint . 2013

deformation quantization with separation of variables of an endomorphism bundle

Karabegov, Alexander;