Chalykh, O orcid.org/0000-0003-4529-2310 and Fairon, M (2020) On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system. Letters in Mathematical Physics, 110 (11). pp. 2893-2940. ISSN 0377-9017
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer Nature B.V. 2020. This is an author produced version of an article published in Letters in Mathematical Physics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Quivers; Double Poisson brackets; Quasi-Hamiltonian reduction; Ruijsenaars-Schneider system |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/K004999/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 29 Jul 2020 12:38 |
Last Modified: | 10 Aug 2021 00:38 |
Published Version: | https://arxiv.org/abs/1811.08727 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s11005-020-01320-x |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:163804 |