Letters in Mathematical Physics

, Volume 106, Issue 10, pp 1429–1449 | Cite as

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

  • L. Fehér
  • T. F. Görbe


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.


integrable systems Ruijsenaars–Schneider models compact phase space 

Mathematics Subject Classification

37J35 70H06 37J15 


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsUniversity of SzegedSzegedHungary
  2. 2.Department of Theoretical PhysicsWIGNER RCP, RMKIBudapestHungary

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