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Fedosov, Boris V.

A simple geometrical construction of deformation quantization. (English) Zbl 0812.53034

J. Differ. Geom. 40, No. 2, 213-238 (1994).
The paper introduces a construction for *-products on symplectic manifolds via Weyl bundles. This is an alternative to the method of M. De Wilde and P. B. A. Lecomte [Lett. Math. Phys. 7, No. 6, 487–496 (1983; Zbl 0526.58023)]. Induced actions of the symplectic group and quantization are considered.
Reviewer: Christian Günther (Libby)

Cited in 21 Reviews
Cited in 195 Documents

MSC:

53D55 Deformation quantization, star products
53D05 Symplectic manifolds (general theory)

Keywords:

star-products; quantization; deformation quantization

Citations:

Zbl 0526.58023
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\textit{B. V. Fedosov}, J. Differ. Geom. 40, No. 2, 213--238 (1994; Zbl 0812.53034)
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References:

[1] F. Bayen, M. Fato, C. Fronsdal, A. Lichnerovicz and D. Sternheimer, Deformation theory and quantization, Ann. Phys. III (1978) 61-151. · Zbl 0377.53025
[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. · Zbl 0526.58023
[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. · Zbl 0635.58019
[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). · Zbl 0765.53023
[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. · Zbl 0672.58011
[8] H. Omori, Y. Macda and A. Yoshioka, Weyl manifolds and deformation quantization, Advances in Math. (China) 85 (1991) 224-255. · Zbl 0734.58011
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