On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models

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dc.creatorFeher, L.
dc.creatorKlimcik, C.
dc.date2009-01-14
dc.date2009-04-02
dc.date.accessioned2026-07-07T13:03:11Z
dc.date.available2026-07-07T13:03:11Z
dc.descriptionWe consider two families of commuting Hamiltonians on the cotangent bundle of the group GL(n,C), and show that upon an appropriate single symplectic reduction they descend to the spectral invariants of the hyperbolic Sutherland and of the rational Ruijsenaars-Schneider Lax matrices, respectively. The duality symplectomorphism between these two integrable models, that was constructed by Ruijsenaars using direct methods, can be then interpreted geometrically simply as a gauge transformation connecting two cross sections of the orbits of the reduction group.
dc.description16 pages, v2: comments and references added at the end of the text
dc.identifierhttps://arxiv.org/abs/0901.1983
dc.identifierhttp://arxiv.org/abs/0901.1983
dc.identifierJ. Phys. A: Math. Theor. 42 (2009) 185202
dc.identifierdoi:10.1088/1751-8113/42/18/185202
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/226709
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.subjectExactly Solvable and Integrable Systems
dc.titleOn the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models
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