RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


SIGMA, 2011, Volume 7, 067, 26 pages (Mi sigma625)  

This article is cited in 8 scientific papers (total in 8 papers)

$1+1$ Gaudin Model

Andrei V. Zotov

Institute of Theoretical and Experimental Physics, Moscow, Russia

Abstract: We study $1+1$ field-generalizations of the rational and elliptic Gaudin models. For $sl(N)$ case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic curve. In $sl(2)$ case we study the equations in detail and find the corresponding Hamiltonian densities. The $n$-site model describes $n$ interacting Landau–Lifshitz models of magnets. The interaction depends on position of the sites (marked points on the curve). We also analyze the $2$-site case in its own right and describe its relation to the principal chiral model. We emphasize that $1+1$ version impose a restriction on a choice of flows on the level of the corresponding $0+1$ classical mechanics.

Keywords: integrable systems; field theory; Gaudin models

DOI: https://doi.org/10.3842/SIGMA.2011.067

Full text: PDF file (521 kB)
Full text: http://emis.mi.ras.ru/journals/SIGMA/2011/067/
References: PDF file   HTML file

Bibliographic databases:

ArXiv: 1012.1072
Document Type: Article
MSC: 14H70; 33E05; 37K20; 37K10
Received: January 29, 2011; in final form July 3, 2011; Published online July 13, 2011
Language: English

Citation: Andrei V. Zotov, “$1+1$ Gaudin Model”, SIGMA, 7 (2011), 067, 26 pp.

Citation in format AMSBIB
\Bibitem{Zot11}
\by Andrei V.~Zotov
\paper $1+1$ Gaudin Model
\jour SIGMA
\yr 2011
\vol 7
\papernumber 067
\totalpages 26
\mathnet{http://mi.mathnet.ru/sigma625}
\crossref{https://doi.org/10.3842/SIGMA.2011.067}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2861209}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000292747400001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855209933}


Linking options:
  • http://mi.mathnet.ru/eng/sigma625
  • http://mi.mathnet.ru/eng/sigma/v7/p67

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. Andrey M. Levin, Mikhail A. Olshanetsky, Andrey V. Smirnov, Andrei V. Zotov, “Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles”, SIGMA, 8 (2012), 095, 37 pp.  mathnet  crossref  mathscinet
    2. Levin A. Olshanetsky M. Smirnov A. Zotov A., “Characteristic Classes and Hitchin Systems. General Construction”, Commun. Math. Phys., 316:1 (2012), 1–44  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Levin A. Olshanetsky M. Smirnov A. Zotov A., “Characteristic Classes of Sl(N, C)-Bundles and Quantum Dynamical Elliptic R-Matrices”, J. Phys. A-Math. Theor., 46:3 (2013), 035201  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. A. V. Zotov, A. V. Smirnov, “Modifications of bundles, elliptic integrable systems, and related problems”, Theoret. and Math. Phys., 177:1 (2013), 1281–1338  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Marshakov A., “Tau-Functions for Quiver Gauge Theories”, J. High Energy Phys., 2013, no. 7, 068  crossref  mathscinet  zmath  isi  elib  scopus
    6. Mironov, A., Morozov, A., Runov, B., Zenkevich, Y., Zotov, A., “Spectral dualities in XXZ spin chains and five dimensional gauge theories”, Journal of High Energy Physics, 2013:12 (2013)  crossref  mathscinet  scopus
    7. A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Classification of isomonodromy problems on elliptic curves”, Russian Math. Surveys, 69:1 (2014), 35–118  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. Levin A., Olshanetsky M., Zotov A., “Classical Integrable Systems and Soliton Equations Related To Eleven-Vertex R-Matrix”, Nucl. Phys. B, 887 (2014), 400–422  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
    Number of views:
    This page:246
    Full text:29
    References:15

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019