Geodesic
The correspondence principle in Abelian Lagrangian geometry
Izvestiya. Mathematics, Tome 65 (2001) no. 4, pp. 823-834 
N. A. Tyurin. The correspondence principle in Abelian Lagrangian geometry. Izvestiya. Mathematics, Tome 65 (2001) no. 4, pp. 823-834. http://geodesic.mathdoc.fr/item/IM2_2001_65_4_a9/
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     title = {The correspondence principle in {Abelian} {Lagrangian} geometry},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Ashtekar A., Schilling T., Geometrical formulation of quantum mechanics, E-print gr-qc/9706069 | MR

[2] Gorodentsev A., Tyurin A., ALAG (Abelian Lagrangian Algebraic Geometry), Preprint 00-7, Max-Planck-Inst. für Math., Bonn

[3] Khart N., Geometricheskoe kvantovanie v deistvii, Mir, M., 1985 | MR

[4] Kirillov A. A., “Geometricheskoe kvantovanie”, Itogi nauki i tekhniki, 4, VINITI, M., 1985, 141–178 | MR

[5] Schilling T., Geometry of quantum mechanics, Doctoral thesis, Penn State University, 1996

[6] Tyurin A. N., Geometric quantization and mirror symmetry, Preprint 99-22, Warwick

[7] Tyurin A. N., Complexification of Bohr–Sommerfeld conditions, Preprint No 15, Math. Inst. Univ. of Oslo, 1999