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Trigonometric and Elliptic Ruijsenaars–Schneider Systems on the Complex Projective Space

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Abstract

We present a direct construction of compact real forms of the trigonometric and elliptic \({n}\)-particle Ruijsenaars–Schneider systems whose completed center-of-mass phase space is the complex projective space \({{\mathbb{CP}}^{n-1}}\) with the Fubini–Study symplectic structure. These systems are labeled by an integer \({p\in\{1,\ldots,n-1\}}\) relative prime to \({n}\) and a coupling parameter \({y}\) varying in a certain punctured interval around \({p\pi/n}\). Our work extends Ruijsenaars’s pioneering study of compactifications that imposed the restriction \({0 < y < \pi/n}\), and also builds on an earlier derivation of more general compact trigonometric systems by Hamiltonian reduction.

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Authors and Affiliations

  1. Department of Theoretical Physics, University of Szeged, Tisza Lajos krt 84-86, Szeged, 6720, Hungary

    L. Fehér & T. F. Görbe

  2. Department of Theoretical Physics, WIGNER RCP, RMKI, P.O.B. 49, Budapest, 1525, Hungary

    L. Fehér

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  1. L. Fehér
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  2. T. F. Görbe
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Correspondence to T. F. Görbe.

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Fehér, L., Görbe, T.F. Trigonometric and Elliptic Ruijsenaars–Schneider Systems on the Complex Projective Space. Lett Math Phys 106, 1429–1449 (2016). https://doi.org/10.1007/s11005-016-0877-z

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  • DOI: https://doi.org/10.1007/s11005-016-0877-z

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