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Spin Ruijsenaars–Schneider Models from Reduction

  • PHYSICS OF ELEMENTARY PARTICLES AND ATOMIC NUCLEI. THEORY
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Abstract

Spin Ruijsenaars–Schneider model introduced by Krichever and Zabrodin is a generalisation of a finite-dimensional integrable system due to Ruijsenaars and Schneider, where particles carry additional internal degrees of freedom. We review how a Hamiltonian structure of the spin model with the hyperbolic potential can be obtained by means of Poisson reduction applied to a specially chosen Poisson manifold.

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REFERENCES

  1. I. Krichever and A. Zabrodin, “Spin generalization of the Ruijsenaars–Schneider model, non-Abelian 2-d Toda chain and representations of Sklyanin algebra,” Russ. Math. Surv. 50, 1101 (1995); hep-th/9505039. https://doi.org/10.1070/RM1995v050n06ABEH002632

    Article  MATH  Google Scholar 

  2. G. E. Arutyunov and S. A. Frolov, “On Hamiltonian structure of the spin Ruijsenaars–Schneider model,” J. Phys. A 31, 4203 (1998); hep-th/9703119. https://doi.org/10.1088/0305-4470/31/18/010

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  3. O. Chalykh and M. Fairon, “On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system,” arXiv: 1811.08727 [math-ph].

  4. G. Arutyunov, R. Klabbers, and E. Olivucci, “Quantum trace formulae for the integrals of the hyperbolic Ruijsenaars–Schneider model,” J. High Energy Phys. 1905, 069 (2019); arXiv: 1902.06755 [hep-th]. https://doi.org/10.1007/JHEP05(2019)069

  5. G. Arutyunov and E. Olivucci, “Hyperbolic spin Ruijsenaars–Schneider model from Poisson reduction,” arXiv: 1906.02619 [hep-th].

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Hamburg, 22761, Hamburg, Germany

    G. Arutyunov

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  1. G. Arutyunov
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Correspondence to G. Arutyunov.

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Arutyunov, G. Spin Ruijsenaars–Schneider Models from Reduction. Phys. Part. Nuclei Lett. 17, 730–733 (2020). https://doi.org/10.1134/S1547477120050027

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  • DOI: https://doi.org/10.1134/S1547477120050027

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