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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 129, Number 2, Pages 327–332
DOI: https://doi.org/10.4213/tmf539 (Mi tmf539) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Self-Dual Hamiltonians as Deformations of Free Systems

A. D. Mironovab

a P. N. Lebedev Physical Institute, Russian Academy of Sciences
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
Full-text PDF (168 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf539
Abstract: We formulate the problem of finding self-dual Hamiltonians (associated with integrable systems) as deformations of free systems given on various symplectic manifolds and discuss several known explicit examples including the recently found double elliptic Hamiltonians. We consider self-duality as the basic principle, while duality in integrable systems (of the Toda/Calogero/Ruijsenaars type) comes as a secondary notion (degenerations of self-dual systems).
English version:
Theoretical and Mathematical Physics, 2001, Volume 129, Issue 2, Pages 1581–1585
DOI: https://doi.org/10.1023/A:1012843409301
Bibliographic databases:
Language: Russian
Citation: A. D. Mironov, “Self-Dual Hamiltonians as Deformations of Free Systems”, TMF, 129:2 (2001), 327–332; Theoret. and Math. Phys., 129:2 (2001), 1581–1585
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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\pages 1581--1585
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Linking options:
  • https://www.mathnet.ru/eng/tmf539
  • https://doi.org/10.4213/tmf539
  • https://www.mathnet.ru/eng/tmf/v129/i2/p327
    • This publication is cited in the following 7 articles:
    1. A. Mironov, A. Morozov, “On the status of DELL systems”, Nuclear Physics B, 999 (2024), 116448  crossref
    2. Grekov A. Zotov A., “On Cherednik and Nazarov-Sklyanin Large N Limit Construction For Integrable Many-Body Systems With Elliptic Dependence on Momenta”, J. High Energy Phys., 2021, no. 12, 62  crossref  mathscinet  isi
    3. Grekov A. Zotov A., “Characteristic Determinant and Manakov Triple For the Double Elliptic Integrable System”, SciPost Phys., 10:3 (2021), 055  crossref  mathscinet  isi
    4. Mironov A. Morozov A. Zenkevich Y., “Duality in Elliptic Ruijsenaars System and Elliptic Symmetric Functions”, Eur. Phys. J. C, 81:5 (2021), 461  crossref  isi  scopus
    5. Awata H. Kanno H. Mironov A. Morozov A., “On a Complete Solution of the Quantum Dell System”, J. High Energy Phys., 2020, no. 4, 212  crossref  mathscinet  isi
    6. Mironov A. Morozov A. Shakirov Sh. Sleptsov A., “Interplay Between Macdonald and Hall-Littlewood Expansions of Extended Torus Superpolynomials”, J. High Energy Phys., 2012, no. 5, 070  crossref  mathscinet  zmath  isi  scopus  scopus
    7. A. D. Mironov, “Integrability in String/Field Theories and Hamiltonian Flows in the Space of Physical Systems”, Theoret. and Math. Phys., 135:3 (2003), 814–827  mathnet  crossref  crossref  mathscinet  zmath  isi
    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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    References:51
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