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Teoreticheskaya i Matematicheskaya Fizika, 1997, Volume 113, Number 3, Pages 369–383
DOI: https://doi.org/10.4213/tmf1086 (Mi tmf1086) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Representations of general commutation relations

V. V. Vedenyapina, O. V. Mingalevb, I. V. Mingalevb

a M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
b Polar Geophysical Institute
Full-text PDF (268 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf1086
Abstract: 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.
Received: 14.12.1995
Revised: 16.04.1997
English version:
Theoretical and Mathematical Physics, 1997, Volume 113, Issue 3, Pages 1508–1519
DOI: https://doi.org/10.1007/BF02634511
Bibliographic databases:
Language: Russian
Citation: V. V. Vedenyapin, O. V. Mingalev, I. V. Mingalev, “Representations of general commutation relations”, TMF, 113:3 (1997), 369–383; Theoret. and Math. Phys., 113:3 (1997), 1508–1519
Citation in format AMSBIB
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\paper Representations of general commutation relations
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\pages 369--383
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  • https://www.mathnet.ru/eng/tmf/v113/i3/p369
    • This publication is cited in the following 3 articles:
    1. Kalmetev R.Sh., Orlov Yu.N., Sakbaev V.Zh., “Generalized Coherent States Representation”, Lobachevskii J. Math., 42:11, SI (2021), 2608–2614  crossref  isi
    2. Kinetic Boltzmann, Vlasov and Related Equations, 2011, 289  crossref
    3. V. V. Vedenyapin, Yu. N. Orlov, “Conservation laws for polynomial Hamiltonians and for discrete models of the Boltzmann equation”, Theoret. and Math. Phys., 121:2 (1999), 1516–1523  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:71
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