## 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 - 1-Oct-2016 |

Externally published | Yes |

## Keywords

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