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

L. Fehér, T. F. Görbe*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1429-1449
Number of pages21
JournalLetters in Mathematical Physics
Issue number10
Publication statusPublished - 1-Oct-2016
Externally publishedYes


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

Cite this