Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






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


Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 129, Number 2, Pages 258–277
DOI: https://doi.org/10.4213/tmf535
(Mi tmf535)
 

This article is cited in 13 scientific papers (total in 13 papers)

Integrable Many-Body Systems via the Inosemtsev Limit

A. V. Zotovab, Yu. B. Chernyakova

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b Moscow Institute of Physics and Technology
References:
Abstract: The Inozemtsev limit (IL), or the scaling limit, is known as a procedure applied to the elliptic Calogero-Moser model. It is a combination of the trigonometric limit, infinite shifts of particle coordinates, and coupling-constant rescalings. This results in an interaction of the exponential type. We show that the IL applied to the $sl(N,\mathbb C)$ elliptic Euler–Calogero–Moser model and to the elliptic Gaudin model produces new Toda-like systems of $N$ interacting particles endowed with additional degrees of freedom corresponding to a coadjoint orbit of $sl(n,\mathbb C)$. The limits corresponding to the complete degeneration of the orbital degrees of freedom lead to recovering only the known periodic and nonperiodic Toda systems. We classify the systems appearing in the IL in the $sl(3,\mathbb C)$ case. This classification is represented on a two-dimensional plane of parameters describing infinite shifts of particle coordinates. This space is subdivided into symmetric domains. In this picture, a mixture of the Toda and trigonometric Calogero-Sutherland potentials emerges on lower-dimensional domain walls. Because of obvious symmetries, this classification can be generalized to an arbitrary number of particles. We also apply the IL to the $sl(2,\mathbb C)$ elliptic Gaudin model on a two-punctured elliptic curve and discuss the main properties of its possible limits. The limits of Lax matrices are also considered.
English version:
Theoretical and Mathematical Physics, 2001, Volume 129, Issue 2, Pages 1526–1542
DOI: https://doi.org/10.1023/A:1012835207484
Bibliographic databases:
Language: Russian
Citation: A. V. Zotov, Yu. B. Chernyakov, “Integrable Many-Body Systems via the Inosemtsev Limit”, TMF, 129:2 (2001), 258–277; Theoret. and Math. Phys., 129:2 (2001), 1526–1542
Citation in format AMSBIB
\Bibitem{ZotChe01}
\by A.~V.~Zotov, Yu.~B.~Chernyakov
\paper Integrable Many-Body Systems via the Inosemtsev Limit
\jour TMF
\yr 2001
\vol 129
\issue 2
\pages 258--277
\mathnet{http://mi.mathnet.ru/tmf535}
\crossref{https://doi.org/10.4213/tmf535}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1904799}
\zmath{https://zbmath.org/?q=an:1029.37037}
\transl
\jour Theoret. and Math. Phys.
\yr 2001
\vol 129
\issue 2
\pages 1526--1542
\crossref{https://doi.org/10.1023/A:1012835207484}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000173055900008}
Linking options:
  • https://www.mathnet.ru/eng/tmf535
  • https://doi.org/10.4213/tmf535
  • https://www.mathnet.ru/eng/tmf/v129/i2/p258
  • This publication is cited in the following 13 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
    Statistics & downloads:
    Abstract page:468
    Full-text PDF :240
    References:63
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024