Homogeneous fedosov star products on cotangent bundles I: Weyl and standard ordering with differential operator representation

Communications in Mathematical Physics

Volumn 198, Issue 2, 1998, Pages 363-396

  Bordemann, Martin ^a   Neumaier, Nikolai ^a   Waldmann, Stefan ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032271706     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050481     Document Type: Article

References (25)

1. Agarwal, G. S., Wolf, E.: Calculus for Functions of Noncommuting Operators and General Phase-Space Methods in Quantum Mechanics. I. Mapping Theorems and Ordering of Functions of Noncommuting Operators. Phys. Rev. D 2, 10, 2161-2188 (1970)
2. Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., Sternheimer, D.: Deformation Theory and Quantization. Annals of Physics 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., Neumaier, N., Waldmann, S.: Homogeneous Fedosov Star Products on Cotangent Bundles II: GNS Representations, the WKB Expansion, and Applications. Preprint Univ. Freiburg FR-THEP-97/23, November 1997, and q-alg/9711016
5. Bordemann, M., Waldmann, S.: A Fedosov Star Product of Wick Type for Kähler manifolds. Lett. Math. Phys. 41, 243-253 (1997)
6. Bordemann, M., Waldmann, S.: Formal GNS Construction and States in Deformation Quantization. Commun. Math. Phys. 195, 549-583 (1998)
7. Bordemann, M., Waldmann, S.: Formal GNS Construction and WKB Expansion in Deformation Quantization. In: Sternheimer, D., Rawnsley, J., Gutt, S.: Deformation Theory and Symplectic Geometry. Mathematical Physics Studies 20, Dordrecht: Kluwer, 1997, pp. 315-319
8. Cahen, M., Gutt, S.: Regular * Representations of Lie Algebras. Lett. Math. Phys. 6, 395-404 (1982)
9. Connes, A., Flato, M., Sternheimer, D.: Closed Star Products and Cyclic Cohomology Lett. Math. Phys. 24, 1-12 (1992)
10. DeWilde, M., Lecomte, P. B. A.: Star Products on Cotangent Bundles. Lett. Math. Phys. 7, 235-241 (1983)
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.: Formal Deformations of the Poisson Lie Algebra of a Symplectic Manifold and Star Products. Existence, Equivalence, Derivations. In: Hazewinkel, M., Gerstenhaber, M. (eds): Deformation Theory of Algebras and Structures and Applications. Dordrecht: Kluwer, 1988
13. Drinfel'd, V. G.: On constant quasiclassical solutions of the Yang-Baxter quantum equation. Soviet Math. Dokl. 28, 667-671 (1983)
14. Emmrich, C., Weinstein, A.: The differential geometry of Fedosov's quantization. In: Brylinski, J.-L., Brylinski, R., Guillemin, V., Kac, V. (eds): Lie Theory and Geometry, in Honor of B. Konstant. Boston, Basel: Birkhäuser, 1994
15. Fedosov, B.: A Simple Geometrical Construction of Deformation Quantization. J. Diff. Geom. 40, 213-238 (1994)
16. Fedosov, B.: Deformation Quantization and Index Theory. Berlin: Akademie Verlag, 1996
17. Gutt, S.: An explicit *-Product on the cotangent bundle of a Lie Group. Lett. Math. Phys. 7, 249-258 (1983)
18. Nest, R., Tsygan, B.: Algebraic Index Theorem. Commun. Math. Phys. 172, 223-262 (1995)
19. Nest, R., Tsygan, B.: Algebraic Index Theorem for Families. Adv. Math. 113, 151-205 (1995)
20. Pflaum, M. J.: Local Analysis of Deformation Quantization. Ph.D. thesis, Fakultät für Mathematik der Ludwig-Maximilians-Universität, München, 1995
21. Pflaum, M. J.: The Normal Symbol on Riemannian Manifolds. New York J. Math. 4, 97-125 (1998)
22. Underhill, J.: Quantization on a manifold with connection. J. Math. Phys. 19, 1932-1935 (1978)
23. Widom, H.: Families of Pseudodifferential Operators. In: Gohberg, I., Kac, M. (eds): Topics in Functional Analysis. New York: Academic Press, 1978
24. Widom, H.: A Complete Symbol Calculus for Pseudodifferential Operators. Bull. Sci. Math. 104, 19-63 (1980)
25. Woodhouse, N.: Geometric Quantization. Oxford: Clarendon Press, 1980