Journal of Differential Geometry

A simple geometrical construction of deformation quantization

Boris V. Fedosov

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J. Differential Geom., Volume 40, Number 2 (1994), 213-238.

First available in Project Euclid: 26 June 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58F06
Secondary: 58F05 81S10: Geometry and quantization, symplectic methods [See also 53D50]


Fedosov, Boris V. A simple geometrical construction of deformation quantization. J. Differential Geom. 40 (1994), no. 2, 213--238. doi:10.4310/jdg/1214455536.

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  • [1] F. Bayen, M. Fato, C. Fronsdal, A. Lichnerovicz and D. Sternheimer, Deformation theory and quantization, Ann. Phys. III (1978) 61-151.
  • [2] M.De Wilde and P. B. A. Lecomte, Existence of star-product and offormal deformations in Poisson Lie algebra of arbitrary symplectic manifold, Lett. Math. Phys. 7 (1983) 487-496.
  • [3] B. Fedosov, Formal quantization, Some Topics of Modern Math, and Their Appl. to Problems of Math. Phys., Moscow, 1985, pp.129-136.
  • [4] B. Fedosov, Formal quantization, Quantization and index, Dokl. Akad. Nauk. SSSR 291 (1986) 82-86, English transl. in Soviet Phys. Dokl. 31 (1986) 877-878.
  • [5] B. Fedosov, Formal quantization, An index theorem in the algebra of quantum observables, Dokl. Akad. Nauk SSSR 305 (1989) 835-839, English transl. in Soviet Phys. Dokl. 34 (1989) 318-321.
  • [6] A. Masmoudi, Ph.D. Thesis, Univ. de Metz (1992).
  • [7] D. Melotte, Invariant deformations of the Poisson Lie algebra of a symplectic manifold and star-products, Deformation Theory of Algebras and Structures and Applica- tions, Ser. C: Math, and Phys. Sci., Vol. 247, Kluwer Acad. PubL, Dordrecht, 1988, 961-972.
  • [8] H. Omori, Y. Macda and A. Yoshioka, Weyl manifolds and deformation quantization, Advances in Math. (China) 85 (1991) 224-255.