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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 4, Pages 191–204 (Mi izv353)  
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

Full text: PDF file (1239 kB)
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English version:
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
\Bibitem{Tyu01}
\by N.~A.~Tyurin
\paper The correspondence principle in Abelian Lagrangian geometry
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 4
\pages 191--204
\mathnet{http://mi.mathnet.ru/izv353}
\crossref{https://doi.org/10.4213/im353}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1857716}
\zmath{https://zbmath.org/?q=an:1034.53094}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 4
\pages 823--834
\crossref{https://doi.org/10.1070/IM2001v065n04ABEH000353}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-27844567810}


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  • https://doi.org/10.4213/im353
  • http://mi.mathnet.ru/eng/izv/v65/i4/p191

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. A. Tyurin, “Dynamical correspondence in algebraic Lagrangian geometry”, Izv. Math., 66:3 (2002), 611–629  mathnet  crossref  crossref  mathscinet  zmath
    2. N. A. Tyurin, “Irreducibility of the ALG(a)-Quantization”, Proc. Steklov Inst. Math., 241 (2003), 249–255  mathnet  mathscinet  zmath
    3. N. A. Tyurin, “Letter to the editors”, Izv. Math., 68:3 (2004), 643–644  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. N. A. Tyurin, “Algebraic Lagrangian geometry: three geometric observations”, Izv. Math., 69:1 (2005), 177–190  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. N. A. Tyurin, “Existence theorem for the moduli space of Bohr–Sommerfeld Lagrangian cycles”, Russian Math. Surveys, 60:3 (2005), 572–574  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    		• Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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