New compact forms of the trigonometric Ruijsenaars-Schneider system

L. Fehér, T. J. Kluck

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The reduction of the quasi-Hamiltonian double of SU(n) that has been shown to underlie Ruijsenaars' compactified trigonometric n-body system is studied in its natural generality. The constraints contain a parameter y, restricted in previous works to 0 <y <π/. n because Ruijsenaars' original compactification relies on an equivalent condition. It is found that allowing generic 0 <y <π/2 results in the appearance of new self-dual compact forms of two qualitatively different types depending on the value of y. The type (i) cases are similar to the standard case in that the reduced phase space comes equipped with globally smooth action and position variables, and turns out to be symplectomorphic to CPn-1 as a Hamiltonian toric manifold. In the type (ii) cases both the position variables and the action variables develop singularities on a nowhere dense subset. A full classification is derived for the parameter y according to the type (i) versus type (ii) dichotomy. The simplest new type (i) systems, for which π/. n <y <π/(n - 1), are described in some detail as an illustration.

Original languageEnglish
Pages (from-to)97-127
Number of pages31
JournalNuclear Physics B
Volume882
Issue number1
DOIs
Publication statusPublished - 2014

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dichotomies
set theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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New compact forms of the trigonometric Ruijsenaars-Schneider system. / Fehér, L.; Kluck, T. J.

In: Nuclear Physics B, Vol. 882, No. 1, 2014, p. 97-127.

Research output: Contribution to journalArticle

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