Local v-Euler derivations and deligne's characteristic class of fedosov star products and star products of special type

Communications in Mathematical Physics

Volumn 230, Issue 2, 2002, Pages 271-288

  Neumaier, Nikolai ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036026999     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-002-0677-4     Document Type: Article

References (24)

1. Abraham, R., Marsden, J. E.: Foundations of Mechanics. Reading, MA: Addison-Wesley Publishing Company, 1985
2. Bayen, F., Flato, M., Frønsdal, C., Lichnerowicz, A., Sternheimer, D.: Deformation Theory and Quantization. Ann. Phys. 111, Part I: 61-110, Part II: 111-151 (1978)
3. Bertelson, M., Cahen, M., Gutt, S.: Equivalence of star products. Class. Quant. Grav. 14, A93-A107 (1997)
4. Bordemann, M.: Strongly invariant star-products and their phase space reduction. Unpublished notes, 1996
5. Bordemann, M., Nenmaier, N., Waldmann, S.: Homogeneous Fedosov Star Products on Cotangent Bundles I: Weyl and Standard Ordering with Differential Operator Representation. Commun. Math. Phys. 198, 363-396 (1998)
6. Bordemann, M., Neumaier, N., Waldmann, S.: Homogeneous Fedosov Star Products on Cotangent Bundles II: GNS Representations, the WKB Expansion, Traces, and Applications. J. Geom. Phys. 29, 199-234 (1999)
7. Bordemann, M., Waldmann, S.: A Fedosov Star Product of Wick Type for Kähler Manifolds. Lett. Math. Phys. 41, 243-253 (1997)
8. Bordemann, M., Waldmann, S.: Formal GNS Construction and States in Deformation Quantization. Commun. Math. Phys. 195, 549-583 (1998)
9. Connes, A., Flato, M., Sternheimer, D.: Closed Star Products and Cyclic Cohomology. Lett. Math. Phys. 24, 1-12 (1992)
10. Deligne, P.: Déformations de l'Algèbre des Fonctions d'une Variété Symplectique: Comparaison entre Fedosov et DeWilde, Lecomte. Sel. Math., New Series 1 (4), 667-697 (1995)
11. DeWilde, M., 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, 487-496 (1983)
12. DeWilde, M., Lecomte, P. B. A.: Existence of Star-Products revisited. Dedicated to the memory of Professor Gottfried Köthe. Note Math. 10, Suppl. 1, 205-216 (1992)
13. Fedosov, B.: A Simple Geometrical Construction of Deformation Quantization. J. Diff. Geom. 40, 213-238 (1994)
14. Fedosov, B.: Deformation Quantization and Index Theory. Berlin: Akademie Verlag, 1996
15. Gutt, S., Rawnsley, J.: Equivalence of star products on a symplectic manifold; An introduction to Deligne's Čech cohomology classes. J. Geom. Phys. 29, 347-392 (1999)
16. Halbout, G.: Calcul d'un Invariant de Star-Produit Fermé sur une Variété Symplectique. Commun. Math. Phys. 205, 53-67 (1999)
17. Halbout, G.: Comparaison des déformations selon DeWilde-Lecomte et Fedosov. Expositiones Math. 17, no. 3, 193-205 (1999)
18. Karabegov, A. V.: Deformation Quantization with Separation of Variables on a Kähler Manifold. Commun. Math. Phys. 180, 745-755 (1996)
19. Karabegov, A. V.: Cohomological Classification of Deformation Quantization with Separation of Variables. Lett. Math. Phys. 43, 347-357 (1998)
20. Kontsevich, M.: Deformation Quantization of Poisson Manifolds, I. Preprint, September 1997, q-alg/9709040
21. Kravchenko, O.: Deformation Quantization of Symplectic Fibrations. Preprint, February 1998, math.QA/9802070
22. Nest, R., Tsygan, B.: Algebraic Index Theorem. Commun. Math. Phys. 172, 223-262 (1995)
23. Nest, R., Tsygan, B.: Algebraic Index Theorem for Families. Adv. Math. 113, 151-205 (1995)
24. th birthday. Am. Math. Soc. Transl., Ser. 2, 186 (39), 177-194 (1998)