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Teoreticheskaya i Matematicheskaya Fizika, 1997, Volume 113, Number 3, Pages 384–396
DOI: https://doi.org/10.4213/tmf1087
(Mi tmf1087)
 

This article is cited in 6 scientific papers (total in 6 papers)

Quantum Volterra model and universal $R$-matrix

A. V. Antonovab

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Université Pierre & Marie Curie, Paris VI
Full-text PDF (240 kB) Citations (6)
References:
Abstract: In this paper, we explicitly prove that an integrable system solved by the quantum inverse scattering method can be described by a pure algebraic object (universal $R$-matrix) and a proper algebraic representation. For the example of the quantum Volterra model, we construct the $L$-operator and the fundamental $R$-matrix from the universal $R$-matrix for the quantum affine $U_q(\widehat{sl}_2)$ algebra and $q$-oscillator representation for it. In this way, there is an equivalence between the integrable system with the symmetry algebra $\mathcal A$ and the representation of this algebra.
Received: 24.04.1997
English version:
Theoretical and Mathematical Physics, 1997, Volume 113, Issue 3, Pages 1520–1529
DOI: https://doi.org/10.1007/BF02634512
Bibliographic databases:
Language: Russian
Citation: A. V. Antonov, “Quantum Volterra model and universal $R$-matrix”, TMF, 113:3 (1997), 384–396; Theoret. and Math. Phys., 113:3 (1997), 1520–1529
Citation in format AMSBIB
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\by A.~V.~Antonov
\paper Quantum Volterra model and universal $R$-matrix
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\yr 1997
\vol 113
\issue 3
\pages 384--396
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\crossref{https://doi.org/10.4213/tmf1087}
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\zmath{https://zbmath.org/?q=an:0963.37503}
\transl
\jour Theoret. and Math. Phys.
\yr 1997
\vol 113
\issue 3
\pages 1520--1529
\crossref{https://doi.org/10.1007/BF02634512}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000072911400003}
Linking options:
  • https://www.mathnet.ru/eng/tmf1087
  • https://doi.org/10.4213/tmf1087
  • https://www.mathnet.ru/eng/tmf/v113/i3/p384
  • This publication is cited in the following 6 articles:
    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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    Abstract page:493
    Full-text PDF :208
    References:86
    First page:1
     
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