Haworth, S and Ruijsenaars, S (2016) Hilbert space theory for relativistic dynamics with reflection. Special cases. Journal of Integrable Systems, 1 (1). xyw003. ISSN 2058-5985
Abstract
We present and study a novel class of one-dimensional Hilbert space eigenfunction transforms that diagonalize analytic difference operators encoding the (reduced) two-particle relativistic hyperbolic Calogero–Moser dynamics. The scattering is described by reflection and transmission amplitudes t and r with function-theoretic features that are quite different from nonrelativistic amplitudes. The axiomatic Hilbert space analysis in the appendices is inspired by and applied to the attractive two-particle relativistic Calogero–Moser dynamics for a sequence of special couplings. Together with the scattering function u of the repulsive case, this leads to a triple of amplitudes u, t and r satisfying the Yang–Baxter equations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) The authors 2016. 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 contactjournals.permissions@oup.com |
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) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Jul 2016 10:46 |
Last Modified: | 23 Jun 2023 22:10 |
Published Version: | http://doi.org/10.1093/integr/xyw003 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/integr/xyw003 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:102834 |