Görbe, TF and Hallnäs, MA (2018) Quantization and explicit diagonalization of new compactified trigonometric Ruijsenaars–Schneider systems. Journal of Integrable Systems, 3 (1). xyy015. ISSN 2058-5985
Abstract
Recently, Fehér and Kluck discovered, at the level of classical mechanics, new compactified trigonometric Ruijsenaars–Schneider nn-particle systems, with phase space symplectomorphic to the (n−1)(n−1)-dimensional complex projective space. In this article, we quantize the so-called type (i) instances of these systems and explicitly solve the joint eigenvalue problem for the corresponding quantum Hamiltonians by generalising previous results of van Diejen and Vinet. Specifically, the quantum Hamiltonians are realized as discrete difference operators acting in a finite-dimensional Hilbert space of complex-valued functions supported on a uniform lattice over the classical configuration space, and their joint eigenfunctions are constructed in terms of discretized An−1An−1 Macdonald polynomials with unitary parameters.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The authors 2018. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com |
Keywords: | math-ph; math-ph; math.MP; nlin.SI |
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) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 Jan 2019 12:49 |
Last Modified: | 25 Jun 2023 21:41 |
Status: | Published |
Publisher: | Oxford University Press (OUP) |
Identification Number: | 10.1093/integr/xyy015 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:141556 |