Theoretical and Mathematical Physics

, Volume 113, Issue 3, pp 1508–1519 | Cite as

Representations of general commutation relations

  • I. V. Mingalev
  • O. V. Mingalev
  • V. V. Vedenyapin


General commutation relations involving creation, annihilation, and particle number operators are considered. Such commutation relations arise in the context of nonstandard Poisson brackets. All possible types of irreducible representations in which the particle number operator or the product of the creation and annihilation operators has a basis of orthonormal eigenvectors are constructed. The irreducible representations that involve the particle number operator reduce to one of four types and those that do not involve the particle number operator reduce to one of five types.


Linear Operator Irreducible Representation Representation Space Annihilation Operator Classification Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • I. V. Mingalev
    • 1
  • O. V. Mingalev
    • 1
  • V. V. Vedenyapin
    • 2
  1. 1.Polar Geophysical Institute, Kola Science CenterRussian Academy of SciencesApatity, Murmansk RegionRussia
  2. 2.Keldysh Institute for Applied MathematicsRussian Academy of SciencesMoscowRussia

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