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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 6, Pages 55–106 (Mi izv4107)  

This article is cited in 1 scientific paper (total in 1 paper)

Algebra and quantum geometry of multifrequency resonance

M. V. Karasev, E. M. Novikova

Moscow State Institute of Electronics and Mathematics

Abstract: The algebra of symmetries of a quantum resonance oscillator in the case of three or more frequencies is described using a finite (minimal) basis of generators and polynomial relations. For this algebra, we construct quantum leaves with a complex structure (an analogue of classical symplectic leaves) and a quantum Kähler 2-form, a reproducing measure, and also the corresponding irreducible representations and coherent states.

Keywords: frequency resonance, algebra of symmetries, non-linear commutation relations, quantum Kähler forms, coherent states.

DOI: https://doi.org/10.4213/im4107

Full text: PDF file (976 kB)
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English version:
Izvestiya: Mathematics, 2010, 74:6, 1155–1204

Bibliographic databases:

UDC: 517.986+517.958
MSC: 81S10, 53C55, 81Q05, 81R05, 81R30
Received: 22.04.2009
Revised: 28.08.2009

Citation: M. V. Karasev, E. M. Novikova, “Algebra and quantum geometry of multifrequency resonance”, Izv. RAN. Ser. Mat., 74:6 (2010), 55–106; Izv. Math., 74:6 (2010), 1155–1204

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Blagodyreva O., Karasev M., Novikova E., “Cubic algebra and averaged Hamiltonian for the resonance 3: (-1) Penning-ioffe trap”, Russ. J. Math. Phys., 19:4 (2012), 440–448  crossref  mathscinet  zmath  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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