q-Deformed Harmonic Oscillator in Phase Space

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dc.creatorAringazin, A. K.
dc.creatorAringazin, K. M.
dc.creatorBaskoutas, S.
dc.creatorBrodimas, G.
dc.creatorJannussis, A.
dc.creatorVlachos, E.
dc.date1998-11-02
dc.date.accessioned2026-07-07T04:25:28Z
dc.date.available2026-07-07T04:25:28Z
dc.descriptionRelation between Bopp-Kubo formulation and Weyl-Wigner-Moyal symbol calculus, and non-commutative geometry interpretation of the phase space representation of quantum mechanics are studied. Harmonic oscillator in phase space via creation and annihilation operators, both the usual and $q$-deformed, is investigated. We found that the Bopp-Kubo formulation is just non-commuting coordinates representation of the symbol calculus. The Wigner operator for the $q$-deformed harmonic oscillator is shown to be proportional to the 3-axis spherical angular momentum operator of the algebra $su_{q}(2)$. The relation of the Fock space for the harmonic oscillator and double Hilbert space of the Gelfand-Naimark-Segal construction is established. The quantum extension of the classical ergodiicity condition is proposed.
dc.description20 pages, LaTeX2e
dc.identifierhttps://arxiv.org/abs/hep-th/9811027
dc.identifierhttp://arxiv.org/abs/hep-th/9811027
dc.identifierProc. of the Intern. Conf. 'Advances in Fundamental Physics', Olympia, Greece, 27-30 Sept. 1993, Eds. M. Barone and F. Selleri, Hadronic Press, 1995, pp.329-348
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/55763
dc.subjectHigh Energy Physics - Theory
dc.titleq-Deformed Harmonic Oscillator in Phase Space
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