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.

##### MSC:

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 |

##### Keywords:

dequantization
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\textit{V. V. Kozlov} and \textit{O. G. Smolyanov}, Dokl. Math. 85, No. 3, 416--420 (2012; Zbl 1260.81092); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 444, No. 6, 607--611 (2012)

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##### References:

[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 |

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[6] | V. P. Maslov, Quantization of Thermodynamics and Ultrasecondary Quantization (Moscow, 2001) [in Russian]. |

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[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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