A. V. Antonov, “Quantum Volterra model and universal $R$-matrix”, TMF, 113:3 (1997), 384–396; Theoret. and Math. Phys., 113:3 (1997), 1520

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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

$R$ -matrix

A. V. Antonov^ab

^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)

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DOI: https://doi.org/10.4213/tmf1087

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

$R$ -matrix) and a proper algebraic representation. For the example of the quantum Volterra model, we construct the

L

$L$ -operator and the fundamental

R

$R$ -matrix from the universal

R

$R$ -matrix for the quantum affine

U_{q} ({\hat{s l}}_{2})

$U_q(\widehat{sl}_2)$ algebra and

q

$q$ -oscillator representation for it. In this way, there is an equivalence between the integrable system with the symmetry algebra

A

$\mathcal A$ 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

$R$ -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

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\issue 3

\pages 384--396

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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:

Zadnik L., Prosen T., “Quasilocal Conservation Laws in the Quantum Hirota Model”, J. Phys. A-Math. Theor., 50:26 (2017), 265203
H. Boos, F. Gohmann, A. Klümper, Kh. Nirov, A. V. Razumov, “Universal integrability objects”, Theoret. and Math. Phys., 174:1 (2013), 21–39
Silvestron, SD, “Twisted Volterra equation”, Journal of Nonlinear Mathematical Physics, 12 (2005), 295
S. Lombardo, “Inverse Spectral Transform for the $q$ -Deformed Volterra Equation”, Theoret. and Math. Phys., 133:2 (2002), 1539–1548
Hikami, K, “The Baxter equation for quantum discrete Boussinesq equation”, Nuclear Physics B, 604:3 (2001), 580
Hikami, K, “The quantum Volterra model and the lattice sine-Gordon system. Construction of the Baxter Q operator and the integrals of motion”, Journal of the Physical Society of Japan, 68:2 (1999), 380

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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