Fordy, AP orcid.org/0000-0002-2523-0262 (2019) First integrals from conformal symmetries: Darboux–Koenigs metrics and beyond. Journal of Geometry and Physics, 145. 103475. ISSN 0393-0440
Abstract
On spaces of constant curvature, the geodesic equations automatically have higher order integrals, which are just built out of first order integrals, corresponding to the abundance of Killing vectors. This is no longer true for general conformally flat spaces, but in this case there is a large algebra of conformal symmetries. In this paper we use these conformal symmetries to build higher order integrals for the geodesic equations. We use this approach to give a new derivation of the Darboux–Koenigs metrics, which have only one Killing vector, but two quadratic integrals. We also consider the case of possessing one Killing vector and two cubic integrals.
The approach allows the quantum analogue to be constructed in a simpler manner.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Crown Copyright © 2019 Published by Elsevier B.V. All rights reserved. This is an author produced version of a paper published in Journal of Geometry and Physics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Hamiltonian system; Super-integrability; Poisson algebra; Conformal algebra; Quantum integrability; Darboux–Koenigs metrics |
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: | 13 Aug 2019 10:05 |
Last Modified: | 29 Jul 2020 00:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.geomphys.2019.07.006 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:149600 |