Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems

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dc.creatorKlishevich, Sergey M.
dc.creatorPlyushchay, Mikhail S.
dc.date2002-12-10
dc.date2003-09-11
dc.date.accessioned2026-07-07T10:49:31Z
dc.date.available2026-07-07T10:49:31Z
dc.descriptionWe investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the su(2) and sl(2,R) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.
dc.description25 pages; ref added; to appear in J. Phys. A
dc.identifierhttps://arxiv.org/abs/hep-th/0212117
dc.identifierhttp://arxiv.org/abs/hep-th/0212117
dc.identifierJ.Phys.A36:11299-11319,2003
dc.identifierdoi:10.1088/0305-4470/36/44/009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184244
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.subjectQuantum Physics
dc.titleDolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems
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