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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 212, Number 2, Pages 190–212
DOI: https://doi.org/10.4213/tmf10287
(Mi tmf10287)
 

Real Hamiltonian forms of affine Toda field theories: Spectral aspects

V. S. Gerdjikovab, G. G. Grahovskic, A. A. Stefanovad

a Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
b Institute for Advanced Physical Studies, Sofia, Bulgaria
c Department of Mathematical Sciences, University of Essex, Colchester, United Kingdom
d Faculty of Mathematics and Informatics, Sofia University "St. Kliment Ohridski", Sofia, Bulgaria
References:
Abstract: The paper is devoted to real Hamiltonian forms of $2$-dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral theory of the associated Lax operators. Real Hamiltonian forms are a special type of “reductions” of Hamiltonian systems, similar to real forms of semisimple Lie algebras. Examples of real Hamiltonian forms of affine Toda field theories related to exceptional complex untwisted affine Kac–Moody algebras are studied. Along with the associated Lax representations, we also formulate the relevant Riemann–Hilbert problems and derive the minimal sets of scattering data that uniquely determine the scattering matrices and the potentials of the Lax operators.
Keywords: real Hamiltonian form, 2-dimensional Toda field theory, exceptional Lie algebras, spectral properties of Lax operators.
Funding agency Grant number
Bulgarian National Science Fund KP-06N42-2
This work is supported by the Bulgarian National Science Fund (grant No. KP-06N42-2).
Received: 16.03.2022
Revised: 16.03.2022
English version:
Theoretical and Mathematical Physics, 2022, Volume 212, Issue 2, Pages 1053–1072
DOI: https://doi.org/10.1134/S0040577922080037
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. S. Gerdjikov, G. G. Grahovski, A. A. Stefanov, “Real Hamiltonian forms of affine Toda field theories: Spectral aspects”, TMF, 212:2 (2022), 190–212; Theoret. and Math. Phys., 212:2 (2022), 1053–1072
Citation in format AMSBIB
\Bibitem{GerGraSte22}
\by V.~S.~Gerdjikov, G.~G.~Grahovski, A.~A.~Stefanov
\paper Real Hamiltonian forms of affine Toda field theories: Spectral aspects
\jour TMF
\yr 2022
\vol 212
\issue 2
\pages 190--212
\mathnet{http://mi.mathnet.ru/tmf10287}
\crossref{https://doi.org/10.4213/tmf10287}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461552}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2022TMP...212.1053G}
\transl
\jour Theoret. and Math. Phys.
\yr 2022
\vol 212
\issue 2
\pages 1053--1072
\crossref{https://doi.org/10.1134/S0040577922080037}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85136617516}
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  • https://www.mathnet.ru/eng/tmf10287
  • https://doi.org/10.4213/tmf10287
  • https://www.mathnet.ru/eng/tmf/v212/i2/p190
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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