On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system

Chalykh, O. and Fairon, M. (2020) On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system. Letters in Mathematical Physics, 110(11), pp. 2893-2940. (doi: 10.1007/s11005-020-01320-x)

Abstract

We suggest a Hamiltonian formulation for the spin Ruijsenaars–Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamiltonian reduction performed on (the cotangent bundle to) a representation space of a framed Jordan quiver. For arbitrary quivers, analogous varieties were introduced by Crawley-Boevey and Shaw, and their interpretation as quasi-Hamiltonian quotients was given by Van den Bergh. Using Van den Bergh’s formalism, we construct commuting Hamiltonian functions on the phase space and identify one of the flows with the spin Ruijsenaars–Schneider system. We then calculate all the Poisson brackets between local coordinates, thus answering an old question of Arutyunov and Frolov. We also construct a complete set of commuting Hamiltonians and integrate all the flows explicitly.

• Item Type: Articles
• Additional Information: The work of the first author (O.C.) was partially supported by EPSRC under Grant EP/K004999/1.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Fairon, Dr Maxime
• Authors: Chalykh, O., and Fairon, M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Letters in Mathematical Physics
• Publisher: Springer
• ISSN: 0377-9017
• ISSN (Online): 1573-0530
• Published Online: 10 August 2020
• Copyright Holders: Copyright © 2020 Springer Nature B.V.
• First Published: First published in Letters in Mathematical Physics 110(11): 2893-2940
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

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