Deformation quantization
Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Exposé no. 789, 21 p. 
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     title = {Deformation quantization},
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     number = {227},
     year = {1995},
     mrnumber = {1321655},
     zbl = {0854.58026},
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     url = {http://archive.numdam.org/item/SB_1993-1994__36__389_0/}
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Weinstein, Alan. Deformation quantization, dans Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Exposé no. 789, 21 p. http://archive.numdam.org/item/SB_1993-1994__36__389_0/

[BFFLS] Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz A., and Sternheimer, D., Deformation theory and quantization, I and II, Ann. Phys. 111, (1977), 61-151. | DOI | MR | Zbl

[Be1] Berezin, F. A., Some remarks about the associated envelope of a Lie algebra, Funct. Anal. Appl. 1, (1967), 91-102. | DOI | MR | Zbl

[Be2] Berezin, F. A., Quantization, Math USSR Izv. 8 (1974), 1109-1165. | DOI | MR | Zbl

[BoG] Boutet De Monvel, L., and Guillemin, V., The spectral theory of Toeplitz operators, Annals. of Math. Studies 99, Princeton University Press, Princeton, 1981. | MR | Zbl

[CaGR] Cahen, M., Gutt, S., and Rawnsley, J., Quantization of Kähler Manifolds. II, Trans. Amer. Math. Soc. 337 (1993), 73-98. | MR | Zbl

[Co] Connes, A., Non-commutative differential geometry, Publ. Math. IHES 62 (1986), 41-144. | DOI | EuDML | Numdam | Zbl

[CoFS] Connes, A., Flato, M., and Sternheimer, D., Closed star-products and cyclic cohomology, Lett. Math. Phys. 24 (1992), 1-12. | DOI | MR | Zbl

[Cz] Czyz, J.,On geometric quantization and its connections with the Maslov theory, Rep. Math. Phys. 15 (1979), 57-97. | DOI | MR | Zbl

[DaP] Dazord, P., and Patissier, G., La première classe de Chern comme obstruction à la quantification asymptotique, Symplectic geometry, groupoids, and integrable systems, Séminaire sud-Rhodanien de géométrie à Berkeley (1989), P. Dazord and A. Weinstein, eds., Springer-MSRI Series (1991), 73-97. | MR | Zbl

[De] Deligne, P., Unpublished letters and lectures at IAS, Princeton, 1993.

[DeL1] De Wilde, M., and Lecomte, P., Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds, Lett. Math. Phys. 7 (1983), 487-496. | DOI | MR | Zbl

[DeL2] De Wilde, M., and Lecomte, P., Formal deformations of the Poisson Lie algebra of a symplectic manifold and star-products. Existence, equivalence, derivations, in M. Hazewinkel and M. Gerstenhaber, eds., Deformation Theory of Algebras and Structures and Applications, Kluwer Acad. Pub., Dordrecht (1988), 897-960. | DOI | MR | Zbl

[DeL3] De Wilde, M., and Lecomte, P., Existence of star-products revisited, Note di Matematica 10, Suppl. 1 (1990), 205-216. | MR | Zbl

[Di] Dirac, P. A. M., The principles of quantum mechanics, Clarenden Press, Oxford, 1930. | JFM | MR | Zbl

[Do] Donin, J., On the quantization of Poisson brackets, Advances in Math. (to appear). | MR | Zbl

[EW] Emmrich, C., and Weinstein, A., The differential geometry of Fedosov's quantization, Lie Theory and Geometry, in Honor of B. Kostant, J.L. Brylinski, R. Brylinski, V. Guillemin, and V. Kac, eds., Progress in Mathematics, Birkhäuser, New York (to appear). | MR | Zbl

[Fe1] Fedosov, B. V., Formal quantization, Some Topics of Modern Mathematics and their Applications to Problems of Mathematical Physics (in Russian), Moscow (1985), 129-136. | MR

[Fe2] Fedosov, B. V., Index theorem in the algebra of quantum observables, Sov. Phys. Dokl. 34 (1989), 318-321. | MR

[Fe3] Fedosov, B. V., A simple geometrical construction of deformation quantization, J. Diff. Geom. (to appear). | MR | Zbl

[Fe4] Fedosov, B. V., Proof of the index theorem for deformation quantization, Advances in Partial Differential Equations, Akademie Verlag, Berlin (to appear). | MR | Zbl

[Fe5] Fedosov, B. V., Reduction and eigenstates in deformation quantization, Advances in Partial Differential Equations, Akademie Verlag, Berlin (to appear). | MR | Zbl

[Fe6] Fedosov, B. V., A trace density in deformation quantization, preprint, Moscow Institute of Physics and Technology, 1994. | MR | Zbl

[FS] Flato, M., and Sternheimer, D., Closedness of star products and cohomologies, Lie Theory and Geometry, in Honor of B. Kostant, J.L. Brylinski, R. Brylinski, V. Guillemin, and V. Kac, eds., Progress in Mathematics, Birkhäuser, New York (to appear). | MR | Zbl

[Ge] Gerstenhaber, M., On the deformation of rings and algebras, Annals of Math., 79 (1964), 59-103. | DOI | MR | Zbl

[Gu] Gutt, S., Equivalence of deformations of twisted products on a symplectic manifold, Lett. Math. Phys. 3 (1979), 495-502. | MR | Zbl

[KM1] Karasev M. V., and Maslov, V. P., Pseudodifferential operators and a canonical operator in general symplectic manifolds, Math. USSR Izvestia 23 (1984), 277-305. | DOI | Zbl

[KM2] Karasev, M. V. and Maslov, V. P., Nonlinear Poisson brackets: geometry and quantization, Translations of mathematical monographs, v. 119, Amer. Math. Soc., Providence, 1993. | MR | Zbl

[L] Lie, S., Theorie der Transformationsgruppen, (Zweiter Abschnitt, unter Mitwirkung von Prof. Dr. Friedrich Engel), Leipzig, Teubner, 1890. | JFM

[LtF] Littlejohn, R. G., and Flynn, W. G., Geometric phases in the asymptotic theory of coupled wave equations, Phys. Rev. A44 (1991), 5239-5256. | DOI | MR

[Mi-Ru] Min-Oo, and Ruh, E., Comparison theorems for compact symmetric spaces, Ann. Sci. École Norm. Sup. 12 (1979), 335-353. | DOI | EuDML | Numdam | MR | Zbl

[Ms] Moser, J., On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 280-296. | DOI | MR | Zbl

[My] Moyal, J., Quantum mechanics as a statistical theory, Proc. Camb. Phil. Soc. 45 (1949), 99-124. | DOI | MR | Zbl

[NT1] Nest, R., and Tsygan, B., Algebraic index theorem, Comm. Math. Phys., (to appear). | MR | Zbl

[NT2] Nest, R., and Tsygan, B., Algebraic index theorem for families, Advances in Math. (to appear). | MR | Zbl

[OMY1] Omori, H., Maeda, Y., and Yoshioka, A., Weyl manifolds and deformation quantization, Advances in Math. 85 (1991), 224-255. | DOI | MR | Zbl

[OMY2] Omori, H., Maeda, Y., and Yoshioka, A., Existence of a closed star-product, Lett. Math. Phys. 26 (1992), 285-294. | DOI | MR | Zbl

[Ri] Rieffel, M. A., Deformation quantization and operator algebras, Proc. Symp. Pure Math. 51 (1990), 411-423. | DOI | MR | Zbl

[Ru] Ruh, E., Cartan connections, Proc.Symp.Pure Math. 54 (1993), 505-519. | DOI | MR | Zbl

[S] Sternberg, S., Celestial Mechanics Part II, W.A. Benjamin, New York, 1969. | Zbl

[Ta] Tamarkin, D. E., Topological invariants of connections on symplectic manifolds, Funct. Anal. Appl. (to appear). | MR | Zbl

[Ts] Tsujishita, T., On variation bicomplexes associated to differential equations, Osaka J. Math 19 (1982), 311-363. | MR | Zbl

[V] Vey, J., Déformation du crochet de Poisson sur une variété symplectique, Comment. Math. Helv. 50 (1975), 421-454. | DOI | EuDML | MR | Zbl

[Wi1] Weinstein, A., Fourier integral operators, quantization, and the spectrum of a Riemannian manifold. Colloque Internationale du Centre National de la Recherche Scientifique No. 237. Géométrie Symplectique et Physique Mathématique (1976), 289-298. | MR | Zbl

[Wi2] Weinstein, A., Noncommutative geometry and geometric quantization, Symplectic Geometry and Mathematical Physics: actes du colloque en l'honneur de Jean-Marie Souriau, P. Donato et al eds., Birkhäuser (1991), 446-461. | DOI | MR | Zbl

[Wy] Weyl, H., The theory of groups and quantum mechanics, Dover, New York, 1931. | JFM | MR | Zbl