### 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 |

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### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Letters in Mathematical Physics*,

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

**Trigonometric and Elliptic Ruijsenaars–Schneider Systems on the Complex Projective Space.** / Fehér, L.; Görbe, T. F.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 106, no. 10, pp. 1429-1449. https://doi.org/10.1007/s11005-016-0877-z

}

TY - JOUR

T1 - Trigonometric and Elliptic Ruijsenaars–Schneider Systems on the Complex Projective Space

AU - Fehér, L.

AU - Görbe, T. F.

PY - 2016/10/1

Y1 - 2016/10/1

N2 - 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 CPn - 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.

AB - 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 CPn - 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.

KW - compact phase space

KW - integrable systems

KW - Ruijsenaars–Schneider models

UR - http://www.scopus.com/inward/record.url?scp=84982273073&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84982273073&partnerID=8YFLogxK

U2 - 10.1007/s11005-016-0877-z

DO - 10.1007/s11005-016-0877-z

M3 - Article

AN - SCOPUS:84982273073

VL - 106

SP - 1429

EP - 1449

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 10

ER -