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

L. Fehér, T. F. Görbe

Research output: Contribution to journalArticle

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 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
Volume106
Issue number10
DOIs
Publication statusPublished - Oct 1 2016

Fingerprint

Complex Projective Space
Elliptic Systems
Symplectic Structure
Particle System
Barycentre
Compactification
integers
center of mass
Phase Space
constrictions
derivation
Restriction
intervals
Interval
Integer
Form

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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

In: Letters in Mathematical Physics, Vol. 106, No. 10, 01.10.2016, p. 1429-1449.

Research output: Contribution to journalArticle

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