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Hamiltonian aspects of quantum theory. (English. Russian original) Zbl 1260.81092
Dokl. Math. 85, No. 3, 416-420 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 444, No. 6, 607-611 (2012).
From the text: This paper considers Hamiltonian structures related to quantum mechanics. We do not discuss structures used in the quantization of classical Hamiltonian or Lagrangian systems (which was first done by Heisenberg and Feynman); on the contrary, we are mainly interested in structures which make it possible to consider quantum systems as classical (although infinite-dimensional in the most natural cases) Hamiltonian (or Lagrangian) systems. The introduction of such structures can be called the dequantization of a quantum system.

81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
81S10 Geometry and quantization, symplectic methods
70H05 Hamilton’s equations
Full Text: DOI
[1] V. V. Kozlov and O. G. Smolyanov, Doklady Math. 81(3), 476–480 (2010). · Zbl 1210.37046
[2] V. V. Kozlov and O. G. Smolyanov, in Quantum Bio-Informatics, Ed. by L. Accardi, W. Freudenberg, and M. Ohya (World Sci., Singapore, 2011), Vol. 4, pp. 321–337.
[3] V. V. Kozlov and O. G. Smolyanov, Doklady Math. 84(1), 571–575 (2011). · Zbl 1236.81143
[4] F. A. Berezin, The Method of Secondary Quantization (Moscow, 1965) [in Russian].
[5] V. P. Maslov, Complex Markov Chains and Continuum Feynman Integral (Moscow, 1976) [in Russian].
[6] V. P. Maslov, Quantization of Thermodynamics and Ultrasecondary Quantization (Moscow, 2001) [in Russian].
[7] N. N. Bogolyubov and N. N. Bogolyubov, Jr., Introduction to Quantum Statistical Mechanics (Moscow, 1984) [in Russian]. · Zbl 0576.60095
[8] J. Kupsch and O. G. Smolyanov, Infinite Dimension. Anal. Quantum Prob. Rel. Topics 1(2), 285–324 (1998). · Zbl 0913.46059
[9] J. Kupsch and O. G. Smolyanov, Math. Notes 73(1–2), 136–141 (2003). · Zbl 1026.81026
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