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This article is cited in 5 scientific papers (total in 5 papers)
The correspondence principle in Abelian Lagrangian geometry
N. A. Tyurin Moscow State University of Transportation
Abstract:
We present a new idea of quantization of classical mechanical systems, which uses the constructions of [2], [7] and [1]. As a first step, we verify the correspondence between the Poisson brackets on the initial symplectic manifold and on the moduli space of half-weighted Bohr–Sommerfeld Lagrangian cycles of a fixed volume.
DOI:
https://doi.org/10.4213/im353
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Izvestiya: Mathematics, 2001, 65:4, 823–834
Bibliographic databases:
MSC: 53D50, 53C15 Received: 26.09.2000
Citation:
N. A. Tyurin, “The correspondence principle in Abelian Lagrangian geometry”, Izv. RAN. Ser. Mat., 65:4 (2001), 191–204; Izv. Math., 65:4 (2001), 823–834
Citation in format AMSBIB
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\yr 2001
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\issue 4
\pages 823--834
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http://mi.mathnet.ru/eng/izv353https://doi.org/10.4213/im353 http://mi.mathnet.ru/eng/izv/v65/i4/p191
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This publication is cited in the following articles:
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N. A. Tyurin, “Dynamical correspondence in algebraic Lagrangian geometry”, Izv. Math., 66:3 (2002), 611–629
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N. A. Tyurin, “Irreducibility of the ALG(a)-Quantization”, Proc. Steklov Inst. Math., 241 (2003), 249–255
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N. A. Tyurin, “Letter to the editors”, Izv. Math., 68:3 (2004), 643–644
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N. A. Tyurin, “Algebraic Lagrangian geometry: three geometric observations”, Izv. Math., 69:1 (2005), 177–190
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N. A. Tyurin, “Existence theorem for the moduli space of Bohr–Sommerfeld Lagrangian cycles”, Russian Math. Surveys, 60:3 (2005), 572–574
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