Hyperbolic spin Ruijsenaars-Schneider model from Poisson reduction

2019/06/06 by Arutyunov, Gleb, Olivucci, Enrico · 2 citations
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1906.02619

Abstract

We derive a Hamiltonian structure for the N-particle hyperbolic spin Ruijsenaars-Schneider model by means of Poisson reduction of a suitable initial phase space. This phase space is realised as the direct product of the Heisenberg double of a factorisable Lie group with another symplectic manifold that is a certain deformation of the standard canonical relations for Nℓ conjugate pairs of dynamical variables. We show that the model enjoys the Poisson-Lie symmetry of the spin group \rm GL_ℓ(\mathbb C) which explains its superintegrability. Our results are obtained in the formalism of the classical r-matrix and they are compatible with the recent findings on the different Hamiltonian structure of the model established in the framework of the quasi-Hamiltonian reduction applied to a quasi-Poisson manifold.

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• Quantum Trigonometric Spin Ruijsenaars-Schneider Models from K-theoretic Coulomb Branches
• Spin Ruijsenaars-Schneider models are Coulomb branches

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