Hyperbolic Spin Ruijsenaars-Schneider Model from Poisson Reduction
نویسندگان
چکیده
منابع مشابه
The D n Ruijsenaars - Schneider model
The Lax pair of the Ruijsenaars-Schneider model with interaction potential of trigonometric type based on Dn Lie algebra is presented. We give a general form for the Lax pair and prove partial results for small n. Liouville integrability of the corresponding system follows a series of involutive Hamiltonians generated by the characteristic polynomial of the Lax matrix. The rational case appears...
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We study the elliptic Cn and BCn Ruijsenaars-Schneider models which is elliptic generalization of system given in [1]. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parameterized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the syst...
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We construct the classical r-matrix structure for the Lax formulation of BC N Ruijsenaars-Schneider systems proposed in [18]. The r-matrix structure takes a quadratic form similar to the A N Ruijsenaars-Schneider Poisson bracket behavior, although the dy-namical dependence is more complicated. Commuting Hamiltonians stemming from the BC N Ruijsenaars-Schneider Lax matrix are shown to be linear ...
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We study the elliptic C n and BC n Ruijsenaars-Schneider models which is elliptic generalization of system given in [1]. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parameter-ized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the s...
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We 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 Ruijsen...
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ژورنال
عنوان ژورنال: Proceedings of the Steklov Institute of Mathematics
سال: 2020
ISSN: 0081-5438,1531-8605
DOI: 10.1134/s0081543820030037