An application of the reduction method to Sutherland type many-body systems

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Abstract

We study Hamiltonian reductions of the free geodesic motion on a non-compact simple Lie group using as reduction group the direct product of a maximal compact subgroup and the fixed point subgroup of an arbitrary involution commuting with the Cartan involution. In general, we describe the reduced system that arises upon restriction to a dense open submanifold and interpret it as a spin Sutherland system. This dense open part yields the full reduced system in important special examples without spin degrees of freedom, which include the BCn Sutherland system built on 3 arbitrary couplings for m <n positively charged and (n-m) negatively charged particles moving on the half-line.

Original languageEnglish
Title of host publicationGeometric Methods in Physics - 31st Workshop, 2012
PublisherSpringer International Publishing
Pages109-117
Number of pages9
Volume61
ISBN (Print)9783034806442
Publication statusPublished - 2013
Event31st Workshop on Geometric Methods in Physics, WGMP 2012 - Bialowieza, Poland
Duration: Jun 24 2012Jun 30 2012

Publication series

NameTrends in Mathematics
Volume61
ISSN (Print)22970215
ISSN (Electronic)2297024X

Other

Other31st Workshop on Geometric Methods in Physics, WGMP 2012
CountryPoland
CityBialowieza
Period6/24/126/30/12

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Keywords

  • Hamiltonian reduction
  • Integrable many-body systems

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Fehér, L. (2013). An application of the reduction method to Sutherland type many-body systems. In Geometric Methods in Physics - 31st Workshop, 2012 (Vol. 61, pp. 109-117). (Trends in Mathematics; Vol. 61). Springer International Publishing.