### 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 CP^{n} ^{-} ^{1} with the Fubini–Study symplectic structure. These systems are labeled by an integer p∈ { 1 , … , n- 1 } relative prime to n and a coupling parameter y varying in a certain punctured interval around pπ/ n. Our work extends Ruijsenaars’s pioneering study of compactifications that imposed the restriction 0 < y< π/ n, and also builds on an earlier derivation of more general compact trigonometric systems by Hamiltonian reduction.

Original language | English |
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Pages (from-to) | 1429-1449 |

Number of pages | 21 |

Journal | Letters in Mathematical Physics |

Volume | 106 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 1 2016 |

### Keywords

- Ruijsenaars–Schneider models
- compact phase space
- integrable systems

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Fehér, L., & Görbe, T. F. (2016). Trigonometric and Elliptic Ruijsenaars–Schneider Systems on the Complex Projective Space.

*Letters in Mathematical Physics*,*106*(10), 1429-1449. https://doi.org/10.1007/s11005-016-0877-z