Symmetries of anisotropic harmonic oscillators with rational ratios of frequencies and their relations to U(N) and O(N+1)

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dc.creatorBonatsos, Dennis
dc.creatorDaskaloyannis, C.
dc.creatorKolokotronis, P.
dc.creatorLenis, D.
dc.date1997-01-21
dc.date.accessioned2026-07-07T05:41:53Z
dc.date.available2026-07-07T05:41:53Z
dc.descriptionThe concept of bisection of a harmonic oscillator or hydrogen atom, used in the past in establishing the connection between U(3) and O(4), is generalized into multisection (trisection, tetrasection, etc). It is then shown that all symmetries of the N-dimensional anisotropic harmonic oscillator with rational ratios of frequencies (RHO), some of which are underlying the structure of superdeformed and hyperdeformed nuclei, can be obtained from the U(N) symmetry of the corresponding isotropic oscillator with an appropriate combination of multisections. Furthermore, it is seen that bisections of the N-dimensional hydrogen atom, which possesses an O(N+1) symmetry, lead to the U(N) symmetry, so that further multisections of the hydrogen atom lead to the symmetries of the N-dim RHO. The opposite is in general not true, i.e. multisections of U(N) do not lead to O(N+1) symmetries, the only exception being the occurence of O(4) after the bisection of U(3).
dc.description14 pages, LaTeX. To appear in the Proceedings of the 7th Hellenic Symposium on Nuclear Physics (Athens, May 1996)
dc.identifierhttps://arxiv.org/abs/nucl-th/9701039
dc.identifierhttp://arxiv.org/abs/nucl-th/9701039
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/82737
dc.subjectNuclear Theory
dc.titleSymmetries of anisotropic harmonic oscillators with rational ratios of frequencies and their relations to U(N) and O(N+1)
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