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Hamiltonian Approach to Secondary Quantization

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Abstract

Structures and objects used in Hamiltonian secondary quantization are discussed. By the secondary quantization of a Hamiltonian system ℋ, we mean the Schrödinger quantization of another Hamiltonian system ℋ1 for which the Hamiltonian equation is the Schrödinger one obtained by the quantization of the original Hamiltonian system ℋ. The phase space of ℋ1 is the realification ℍR of the complex Hilbert space ℍ of the quantum analogue of ℋ equipped with the natural symplectic structure. The role of a configuration space is played by the maximal real subspace of ℍ.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991, Russia

    V. V. Kozlov

  2. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    O. G. Smolyanov

  3. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, 141700, Russia

    O. G. Smolyanov

Authors
  1. V. V. Kozlov
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  2. O. G. Smolyanov
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Correspondence to O. G. Smolyanov.

Additional information

Original Russian Text © V.V. Kozlov, O.G. Smolyanov, 2018, published in Doklady Akademii Nauk, 2018, Vol. 483, No. 2.

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Kozlov, V.V., Smolyanov, O.G. Hamiltonian Approach to Secondary Quantization. Dokl. Math. 98, 571–574 (2018). https://doi.org/10.1134/S1064562418070098

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  • DOI: https://doi.org/10.1134/S1064562418070098

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