Classification of polarized deformation quantizations

Journal of Geometry and Physics

Volumn 48, Issue 4, 2003, Pages 546-579

  Donin, Joseph ^a  

^a BAR ILAN UNIVERSITY   (Israel)

Author keywords

Deformation quantization; Polarization; Star product; Symplectic manifold

Indexed keywords

EID: 0142169837     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(03)00055-X     Document Type: Article

References (23)

1. Astashkevich, A. On Karabegov's Quantization of Semisimple Coadjoint Orbits: Advances in Geometry, Progr. Math., vol. 172, Birkhäuser, Boston, MA, 1999, 1-18.
2. Bayen F. Flato M. Fronsdal C. Lichnerowicz A. Sternheimer D. Deformation theory and quantization Ann. Phys. 111 1978 61-110
3. Beilinson, A. Bernstein, J. A proof of Jantzen conjectures. I. M. Gelfand Seminar, 1-50, Adv. Soviet Math., 16, Part 1, American Mathematical Society, Providence, RI, 1993.
4. Beilinson, A. Kazhdan, D. Geometric quantization, preprint.
5. Bressler, P. Donin, J. Polarized deformation quantization, math.QA/0007186.
6. Bordemann, M. Neumaier, N. Pflaum, M.J. Waldmann, S. On representations of star product algebras over cotangent spaces on Hermitian line bundles, math.QA/9811055.
7. Bordemann M. Waldmann S. A Fedosov star product of the Wick type for Kähler manifolds Lett. Math. Phys. 413 1997 243-253
8. Bordemann M. Neumaier N. Waldmann S. Homogeneous Fedosov star products on cotangent bundles. I. Weyl and standard ordering with differential operator representation Commun. Math. Phys. 1982 1998 363-396
9. Deligne P. Dèformations de l'Algébre des Fonctions d'une Variété Symplectique: Comparaison entre Fedosov et De Wilde, Lecomte Selecta Mathematica 14 1995 667-697
10. Donin J. On the quantization of Poisson brackets Adv. Math. 1271 1997 73-93
11. Fedosov, B. Deformation Quantization and Index Theory, Academie Verlag, vol. 9.
12. Karabegov A. Deformation quantization with separation of variables on Kähler manifold Commun. Math. Phys. 180 1996 745-755
13. Karabegov A. Cohomological classification of deformation quantizations with separation of variables Lett. Math. Phys. 43 1998 347-357
14. Karabegov, A. Schlichenmaier, M. Almost Kähler Deformation Quantization, math.QA/0102169.
15. Kobayashi, S. Nomizu, K. Foundations of Differential Geometry, vol. II, Interscience, New York, 1969.
16. Kontsevich, M. Deformation quantization of Poisson manifolds, I, q-alg/9709040.
17. Lichnerowicz A. Existence and equivalence of twisted products on a symplectic manifold Lett. Math. Phys. 3 6 1979 495-502
18. Nest R. Tsygan B. Algebraic index theorem for families Adv. Math. 113 1995 151-205
19. Neumaier, N. Universality of Fedosov's Construction for Star Products of Wick Type on Semi-Käler Manifolds, math.QA/0204031.
20. Pflaum M.J. Deformation quantization on cotangent bundles, Coherent states, differential and quantum geometry (Białowieża, 1997) Rep. Math. Phys. 431-2 1999 291-297
21. Rawnsley J.H. Polarization and diagonal quantization Trans. AMS 230 1977 235-255
22. Reshetikhin, N. Yakimov, M. Deformation quantization of Lagrangean fiber bundles, preprint, math/9907164.
23. Xu P. Fedosov's -products and quantum momentum maps Commun. Math. Phys. 197 1998 167-197