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Reduction of quantum analogs of Hamiltonian systems described by Lie algebras to orbits in a coadjoint representation

  • Physics Of Elementary Particles And Field Theory
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Russian Physics Journal Aims and scope

Abstract

A study is made of the possibility of reducing quantum analogs of Hamiltonian systems to Lie algebras. The procedure of reducing classical systems to orbits in a coadjoint representation based on Lie algebra is well-known. An analog of this procedure for quantum systems described by linear differential equations (LDEs) in partial derivatives is proposed here on the basis of the method of noncommutative integration of LDEs. As an example illustrating the procedure, an examination is made of nontrivial systems that cannot be integrated by separation of variables: the Gryachev-Chaplygin hydrostat and the Kovalevskii gyroscope. In both cases, the problem is reduced to a system with a smaller number of variables.

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Authors
  1. Ya. V. Lisitsyn
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  2. A. V. Shapovalov
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Additional information

Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 69–74, May, 1998.

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Lisitsyn, Y.V., Shapovalov, A.V. Reduction of quantum analogs of Hamiltonian systems described by Lie algebras to orbits in a coadjoint representation. Russ Phys J 41, 460–464 (1998). https://doi.org/10.1007/BF02766506

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  • DOI: https://doi.org/10.1007/BF02766506

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