Hidden symmetries of deformed oscillators

Hidden symmetries of deformed oscillators

We associate with each simple Lie algebra a system of second-order differential equations invariant under a non-compact real form of the corresponding Lie group. In the limit of a contraction to a Schrödinger algebra, these equations reduce to a system of ordinary harmonic oscillators. We provide tw...

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Main Authors: Sergey Krivonos, Olaf Lechtenfeld, Alexander Sorin
Format: Article
Language:English
Published: Elsevier 2017-11-01
Series:Nuclear Physics B
Online Access:http://www.sciencedirect.com/science/article/pii/S0550321317302845
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spelling doaj-11475030c93e4194982363ed2e9f4dd72020-11-24T23:30:03ZengElsevierNuclear Physics B0550-32131873-15622017-11-01924C334610.1016/j.nuclphysb.2017.09.003Hidden symmetries of deformed oscillatorsSergey Krivonos0Olaf Lechtenfeld1Alexander Sorin2Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, RussiaInstitut für Theoretische Physik and Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Appelstrasse 2, D-30167 Hannover, GermanyBogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, RussiaWe associate with each simple Lie algebra a system of second-order differential equations invariant under a non-compact real form of the corresponding Lie group. In the limit of a contraction to a Schrödinger algebra, these equations reduce to a system of ordinary harmonic oscillators. We provide two clarifying examples of such deformed oscillators: one system invariant under SO(2,3) transformations, and another system featuring G2(2) symmetry. The construction of invariant actions requires adding semi-dynamical degrees of freedom; we illustrate the algorithm with the two examples mentioned.http://www.sciencedirect.com/science/article/pii/S0550321317302845
collection DOAJ
language English
format Article
sources DOAJ
author Sergey Krivonos
Olaf Lechtenfeld
Alexander Sorin
spellingShingle Sergey Krivonos
Olaf Lechtenfeld
Alexander Sorin
Hidden symmetries of deformed oscillators
Nuclear Physics B
author_facet Sergey Krivonos
Olaf Lechtenfeld
Alexander Sorin
author_sort Sergey Krivonos
title Hidden symmetries of deformed oscillators
title_short Hidden symmetries of deformed oscillators
title_full Hidden symmetries of deformed oscillators
title_fullStr Hidden symmetries of deformed oscillators
title_full_unstemmed Hidden symmetries of deformed oscillators
title_sort hidden symmetries of deformed oscillators
publisher Elsevier
series Nuclear Physics B
issn 0550-3213
1873-1562
publishDate 2017-11-01
description We associate with each simple Lie algebra a system of second-order differential equations invariant under a non-compact real form of the corresponding Lie group. In the limit of a contraction to a Schrödinger algebra, these equations reduce to a system of ordinary harmonic oscillators. We provide two clarifying examples of such deformed oscillators: one system invariant under SO(2,3) transformations, and another system featuring G2(2) symmetry. The construction of invariant actions requires adding semi-dynamical degrees of freedom; we illustrate the algorithm with the two examples mentioned.
url http://www.sciencedirect.com/science/article/pii/S0550321317302845
work_keys_str_mv AT sergeykrivonos hiddensymmetriesofdeformedoscillators
AT olaflechtenfeld hiddensymmetriesofdeformedoscillators
AT alexandersorin hiddensymmetriesofdeformedoscillators
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