Fordy, AP orcid.org/0000-0002-2523-0262 (2018) A Kaluza–Klein reduction of super-integrable systems. Journal of Geometry and Physics, 131. pp. 210-219. ISSN 0393-0440
Abstract
Given a super-integrable system in n degrees of freedom, possessing an integral which is linear in momenta, we use the “Kaluza–Klein construction” in reverse to reduce to a lower dimensional super-integrable system. We give two examples of a reduction from 3 to 2 dimensions. The constant curvature metric (associated with the kinetic energy) is the same in both cases, but with two different super-integrable extensions. For these, we use different elements of the algebra of isometries of the kinetic energy to reduce to 2-dimensions. Remarkably, the isometries of the reduced space can be derived from those of the 3-dimensional space, even though it requires the use of quadratic expressions in momenta.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Elsevier B.V. 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; Kaluza–Klein |
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: | 17 May 2018 09:19 |
Last Modified: | 22 May 2019 00:43 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.geomphys.2018.05.014 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:130924 |