Almost-Kähler deformation quantization

Letters in Mathematical Physics

Volumn 57, Issue 2, 2001, Pages 135-148

  Karabegov, Alexander V ^a   Schlichenmaier, Martin ^b  

^a YEREVAN PHYSICS INSTITUTE   (Armenia)

^b UNIVERSITY OF MANNHEIM   (Germany)

Author keywords

Almost K hler manifold; Deformation quantization; Star product

Indexed keywords

EID: 0038611900     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1017993513935     Document Type: Article

References (34)

1. Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A. and Sternheimer, D.: Deformation theory and quantization, Part I, Lett. Math. Phys. 1 (1977), 521-530; Deformation theory and quantization, Part II and III, Ann. Phys. 111 (1978), 61-110, 111-151.
2. Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A. and Sternheimer, D.: Deformation theory and quantization, Part I, Lett. Math. Phys. 1 (1977), 521-530; Deformation theory and quantization, Part II and III, Ann. Phys. 111 (1978), 61-110, 111-151.
3. Berezin, F. A.: Quantization, Math. USSR-Izv. 8 (1974), 1109-1165.
4. Bordemann, M., Meinrenken, E. and Schlichenmaier, M.: Toeplitz quantization of Kähler manifolds and gl(n), n → ∞ limits, Comm. Math. Phys. 165 (1994), 281-296.
5. Bordemann, M. and Waldmann, St.: A Fedosov star product of the Wick type for Kähler manifolds, Lett. Math. Phys. 41 (1997), 243-253.
6. Borthwick, D. and Uribe, A.: Almost-complex structures and geometric quantization, Math. Res. Lett. 3 (1996), 845-861.
7. Boutet Monvel, L. and Guillemin, V.: The Spectral Theory of Toeplitz Operators, Ann. Math. Stud. 99, Princeton Univ. Press, Princeton, 1981.
8. Cahen, M., Gutt, S. and Rawnsley, J.: Quantization of Kähler manifolds II, Trans. Amer. Math. Soc. 337 (1993), 73-98.
9. Cahen, M., Gutt, S. and Rawnsley, J.: Quantization of Kähler manifolds III, Lett. Math. Phys. 30 (1994), 291-305.
10. Cahen, M., Gutt, S. and Rawnsley, J.: Quantization of Kähler manifolds IV, Lett. Math. Phys. 34 (1995), 159-168.
11. De Wilde, M. and Lecomte, P. B. A.: Existence of star products and of formal deformations of the Poisson-Lie algebra of arbitrary symplectic manifolds, Lett. Math. Phys. 7 (1983), 487-496.
12. Deligne, P.: Deformation de l'algèbre des fonctions d'une variété symplectique: Comparaison entre Fedosov et De Wilde, Lecomte, Selecta Math. (N.S.) 1 (1995), 667-697.
13. Dolgushev, V. A., Lyakhovich, S. L. and Sharapov, A. A.: Wick type deformation quantizations of Fedosov manifolds, hep-th/0101032.
14. Fedosov, B. V.: Deformation Quantization and Index Theory, Akademie-Verlag, Berlin, 1996.
15. Fedosov, B. V.: Deformation quantization and asymptotic operator representation, Funktional Anal. i. Prilozhen. 25 (1990), 184-194. A simple geometric construction of deformation quantization, J. Differential Geom. 40 (1994), 213-238.
16. Fedosov, B. V.: Deformation quantization and asymptotic operator representation, Funktional Anal. i. Prilozhen. 25 (1990), 184-194. A simple geometric construction of deformation quantization, J. Differential Geom. 40 (1994), 213-238.
17. Gelfand, I., Retakh, V. and Shubin, M.: Fedosov manifolds. Adv. in Math. 136 (1998), 104-140.
18. Gutt, S. and Rawnsley, J.: Equivalence of star products on a symplectic manifold; an introduction to Deligne's Čech cohomology classes, J. Geom. Phys. 29 (1999), 347-392.
19. Guillemin, V.: Star products on pre-quantizable symplectic manifolds, Lett. Math. Phys. 35 (1995), 85-89.
20. Guillemin, V. and Uribe, A.: The Laplace operator on the n-th tensor power of a line bundle:eigenvalues which are uniformly bounded in n, Asymptotic Anal. 1 (1988), 105-113.
21. Karabegov, A. V.: Deformation quantization with separation of variables on a Kähler manifold, Comm. Math. Phys. 180 (1996), 745-755.
22. Karabegov, A. V.: Cohomological classification of deformation quantizations with separation of variables, Lett. Math. Phys. 43 (1998), 347-357.
23. Karabegov, A. V.: Pseudo-Kähler quantization on flag manifolds, Comm. Math. Phys. 200 (1999), 355-379.
24. Karabegov, A. V.: On Fedosov's approach to deformation quantization with separation of variables, In: G. Dito and D. Sternheimer, (eds), Conference Moshé Flato 1999 (September 1999, Dijon, France), Kluwer, Acad. Publ., Dordrecht, 2000, math.QA/ 9910137, Vol. 2, pp. 167-176.
25. Karabegov, A. and Schlichenmaier, M.: Identification of Berezin-Toeplitz deformation quantization, math.QA/0006063, to appear in J. Reine Angew. Math. 24. Kontsevich, M.: Deformation quantization of Poisson manifolds, I, q-alg/9709040.
26. Karabegov, A. and Schlichenmaier, M.: Identification of Berezin-Toeplitz deformation quantization, math.QA/0006063, to appear in J. Reine Angew. Math. 24. Kontsevich, M.: Deformation quantization of Poisson manifolds, I, q-alg/9709040.
27. Moreno, G.: *-products on some Kähler manifolds, Lett. Math. Phys. 11 (1986), 361-372.
28. 2 and related spectral analysis, Lett. Math. Phys. 7 (1983), 181-193.
29. Nest, R. and Tsygan, B.: Algebraic index theory, Comm. Math. Phys. 172 (1995), 223-262.
30. Nest, R. and Tsygan, B.: Algebraic index theory for families, Adv. in Math. 113 (1995), 151-205.
31. Omori, H., Maeda, Y. and Yoshioka, A.: Weyl manifolds and deformation quantization, Adv. in Math. 85 (1991), 224-255.
32. Schlichenmaier, M.: Berezin-Toeplitz quantization of compact Kähler manifolds, In: A. Strasburger, S. T. Ali, J.-P. Antoine, J.-P. Gazeau, and A. Odzijewicz (eds),: Quantization, Coherent States and Poisson Structures, Proc. XIV Workshop on Geometric Methods in Physics (Białowieza, Poland, 9-15 July 1995) Polish Scientific Publisher PWN, 1998, pp. 101-115, q-alg/9601016.
33. Schlichenmaier, M.: Deformation quantization of compact Kähler manifolds by Berezin-Toeplitz quantization, In: G. Dito and D. Sternheimer (eds), Conference Moshé Flato 1999 (September 1999, Dijon, France), Kluwer, Acad. Publ., Dordrecht, 2000, math.QA/9910137, Vol. 2, pp. 289-306.
34. Yano, K.: Differential Geometry on Complex and Almost Complex Spaces, Pergamon Press, MacMillan, New York, 1965.