Spheroidal analysis of the generalized MIC-Kepler system

Mardoyan, L. G.

doi:10.1134/1.2121925

Cited by 17 publications

(14 citation statements)

References 33 publications

(23 reference statements)

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“…Such a monopole and instanton solutions are given in [14]. The similar analysis of the systems with axial symmetry is more complicated but more important (the simplest system of this sort, specified with the presence of Dirac monopole was proposed in [15]). Indeed, presented way of the incorporation of the monopole in the spherically symmetric systems does not yield essential change in the system's properties.…”

Section: Resultsmentioning

confidence: 99%

Relationship between quantum-mechanical systems with and without monopoles

2007

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We show that the inclusion of the monopole field in the three-and five-dimensional spherically symmetric quantum mechanical systems, supplied by the addition of the special centrifugal term, does not yield any change in the radial wavefunction and in the functional dependence of the energy spectra on quantum numbers. The only change in the spectrum is the lift of the range of the total and azimuth quantum numbers. The changes in the angular part wavefunction are independent of the specific choice of the (central) potential. We also present the integrable model of the spherical oscillator which is different from the Higgs oscillator.

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Section: Resultsmentioning

confidence: 99%

Relationship between quantum-mechanical systems with and without monopoles

2007

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“…Since C N -Smorodinsky-Winternitz system has manifest U (1) invariance, we could apply its respective reduction procedure related with first Hopf map S 3 /S 1 = S 2 , which is known as Kustaanheimo-Stieffel transformation, for the particular case of N = 2. Such a reduction was performed decade ago [39] and was found to be resulted in the so-called "generalized MICZ-Kepler problem" suggested by Mardoyan a bit earlier [40,41]. However the initial system was considered, it was not specified by the presence of constant magnetic field, furthermore, the symmetry algebra of the reduced system was not obtained there.…”

Section: Kustaanheimo-stiefel Transformationmentioning

confidence: 99%

CN-Smorodinsky–Winternitz system in a constant magnetic field

Shmavonyan

2019

Physics Letters A

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We propose the superintegrable generalization of Smorodinsky-Winternitz system on the Ndimensional complex Euclidian space which is specified by the presence of constant magnetic field. We find out that in addition to 2N Liouville integrals the system has additional functionally independent constants of motion, and compute their symmetry algebra. We perform the Kustaanheimo-Stiefel transformation of C 2 -Smorodinsky-Winternitz system to the (three-dimensional) generalized MICZ-Kepler problem and find the symmetry algebra of the latter one. We observe that constant magnetic field appearing in the initial system has no qualitative impact on the resulting system. * Electronic address: hovhannes.shmavonyan@mail.yerphi.am

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“…The geodesic of the generalized Taub-NUT metrics properly explains the motion of well-separated monopole-monopole interactions which provide non-trivial generalizations of the Kepler and harmonic oscillator systems [3,4,5,6,7,8,9,10,11]. The 5D Kepler systems interacting with su(2) monopoles or Yang-Coulomb monopoles have been investigated in [12,13,14,15,16,17,18,19,20,21,22]. Recently, there is a lot of international research interest in generalizing such monopole models to higher dimensions via different approaches [11,23,24,25,26,27].…”

Section: Introductionmentioning

confidence: 99%

On superintegrable monopole systems

Hoque

Marquette

Zhang

2018

J. Phys.: Conf. Ser.

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Superintegrable systems with monopole interactions in flat and curved spaces have attracted much attention. For example, models in spaces with a Taub-NUT metric are well-known to admit the Keplertype symmetries and provide non-trivial generalizations of the usual Kepler problems. In this paper, we overview new families of superintegrable Kepler, MIC-harmonic oscillator and deformed Kepler systems interacting with Yang-Coulomb monopoles in the flat and curved Taub-NUT spaces. We present their higher-order, algebraically independent integrals of motion via the direct and constructive approaches which prove the superintegrability of the models. The integrals form symmetry polynomial algebras of the systems with structure constants involving Casimir operators of certain Lie algebras. Such algebraic approaches provide a deeper understanding to the degeneracies of the energy spectra and connection between wave functions and differential equations and geometry.

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Spheroidal analysis of the generalized MIC-Kepler system

Cited by 17 publications

References 33 publications

Relationship between quantum-mechanical systems with and without monopoles

Relationship between quantum-mechanical systems with and without monopoles

CN-Smorodinsky–Winternitz system in a constant magnetic field

On superintegrable monopole systems

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