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Zapiski Nauchnykh Seminarov POMI, 2023, Volume 520, Pages 50–123 (Mi znsl7313)  
Baxter $Q$-operators in Ruijsenaars–Sutherland hyperbolic systems: one- and two-particle cases

N. Belousova, S. Derkachova, S. Kharchevbc, S. Khoroshkincd

a Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191023, Russia
b National Research Center “Kurchatov Institute”
c Institute for Information Transmission Problems RAS (Kharkevich Institute), Bolshoy Karetny per. 19, Moscow, 127994, Russia
d National Research University Higher School of Economics
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Abstract: In these notes we review the technique of Baxter $Q$-operators in the Ruijsenaars-Sutherland hyperbolic systems in the cases of one and two particles. Using these operators we show in particular that eigenfunctions of these systems admit two dual integral representations and prove their orthogonality and completeness.
Key words and phrases: Ruijsenaars, Sutherland, Calogero, Baxter $Q$-operator, eigenfunctions, orthogonality, completeness.
Funding agency Grant number
Russian Science Foundation 23-11-00311
23-11-00150
20-12-00195
The work of N. Belousov and S. Derkachov was supported by Russian Science Foundation, project No. 23-11-00311, used for the proof of statements of Section 3. The work of S. Khoroshkin was supported by Russian Science Foundation, project No 23-11-00150, used for the proof of statements of Sections 2.1--2.3. The work of S. Kharchev was supported by Russian Science Foundation, project No 20-12-00195, used for the proof of statements of Section 2.4 and Appendices A, B, C.
Received: 03.07.2023
Document Type: Article
UDC: 517
Language: English
Citation: N. Belousov, S. Derkachov, S. Kharchev, S. Khoroshkin, “Baxter $Q$-operators in Ruijsenaars–Sutherland hyperbolic systems: one- and two-particle cases”, Questions of quantum field theory and statistical physics. Part 29, Zap. Nauchn. Sem. POMI, 520, POMI, St. Petersburg, 2023, 50–123
Citation in format AMSBIB
\Bibitem{BelDerKha23}
\by N.~Belousov, S.~Derkachov, S.~Kharchev, S.~Khoroshkin
\paper Baxter $Q$-operators in Ruijsenaars--Sutherland hyperbolic systems: one- and two-particle cases
\inbook Questions of quantum field theory and statistical physics. Part~29
\serial Zap. Nauchn. Sem. POMI
\yr 2023
\vol 520
\pages 50--123
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7313}
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