|
This article is cited in 11 scientific papers (total in 11 papers)
Hyperbolic Spin Ruijsenaars–Schneider Model from Poisson Reduction
Gleb E. Arutyunovab, Enrico Olivucciab a II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
b Zentrum für Mathematische Physik, Universität Hamburg, Bundesstr. 55, 20146 Hamburg, Germany
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 $N\ell $ conjugate pairs of dynamical variables. We show that the model enjoys the Poisson–Lie symmetry of the spin group $\mathrm {GL}_{\ell }(\mathbb C)$, 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.
Received: August 23, 2019 Revised: October 18, 2019 Accepted: March 30, 2020
Citation:
Gleb E. Arutyunov, Enrico Olivucci, “Hyperbolic Spin Ruijsenaars–Schneider Model from Poisson Reduction”, Modern problems of mathematical and theoretical physics, Collected papers. On the occasion of the 80th birthday of Academician Andrei Alekseevich Slavnov, Trudy Mat. Inst. Steklova, 309, Steklov Math. Inst. RAS, Moscow, 2020, 38–53; Proc. Steklov Inst. Math., 309 (2020), 31–45
Linking options:
https://www.mathnet.ru/eng/tm4089https://doi.org/10.4213/tm4089 https://www.mathnet.ru/eng/tm/v309/p38
|
Statistics & downloads: |
Abstract page: | 191 | Full-text PDF : | 26 | References: | 75 | First page: | 11 |
|