<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:math>-Smorodinsky–Winternitz system in a constant magnetic field

Shmavonyan, Hovhannes

doi:10.1016/j.physleta.2019.01.049

Cited by 11 publications

(20 citation statements)

References 43 publications

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“…In particular, we focus on the interplay of SU(2|1) supersymmetry and hidden symmetry in forming the energy spectrum of this system. An analogous analysis of its purely bosonic sector was performed in [11]. An interesting unique feature of the SU(2|1) C N S.-W. model as compared to other models of SU(2|1) supersymmetric Kähler oscillators 3 is its implicit superconformal SU(2|1, 1) symmetry.…”

Section: Jhep01(2021)015mentioning

confidence: 99%

“…This observation further entailed the construction of a few novel SU(2|1) supersymmetric superintegrable oscillator-like models specified by the interaction with a constant magnetic field. They include superextensions of isotropic oscillators on C N and CP N [7,10], as well as of C N Smorodinsky-Winternitz system in the presence of a constant magnetic field [11] and CP N Rosochatius system [12].…”

Section: Introductionmentioning

confidence: 99%

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Quantum SU(2|1) supersymmetric ℂN Smorodinsky-Winternitz system

Ivanov

Nersessian

Sidorov³

2021

J. High Energ. Phys.

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We study quantum properties of SU(2|1) supersymmetric (deformed $$ \mathcal{N} $$ N = 4, d = 1 supersymmetric) extension of the superintegrable Smorodinsky-Winternitz system on a complex Euclidian space ℂN. The full set of wave functions is constructed and the energy spectrum is calculated. It is shown that SU(2|1) supersymmetry implies the bosonic and fermionic states to belong to separate energy levels, thus exhibiting the “even-odd” splitting of the spectra. The superextended hidden symmetry operators are also defined and their action on SU(2|1) multiplets of the wave functions is given. An equivalent description of the same system in terms of superconformal SU(2|1, 1) quantum mechanics is considered and a new representation of the hidden symmetry generators in terms of the SU(2|1, 1) ones is found.

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Section: Jhep01(2021)015mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum SU(2|1) supersymmetric ℂN Smorodinsky-Winternitz system

Ivanov

Nersessian

Sidorov³

2021

J. High Energ. Phys.

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“…However, there is a more elegant and simple way to construct it. Namely, one has to consider the symmetry algebra of C N +1 -Smorodinsky-Winternitz system [20] with vanishing magnetic field, and to reduce it, by action of the generators N i=0 ı(p i u i −p iū i ), N i=0 u iūi (see the previous Section), to the symmetry algebra of CP N -Rosochatius system.…”

Section: Cp N -Rosochatius Systemmentioning

confidence: 99%

“…On the other hand, rescaling the coordinates and momenta as r 0 z a → z a , π a /r 0 → π a and taking the limit r 0 → ∞, ω a → 0 with r 2 0 ω a = g a kept finite, we arrive at the so-called "C N -Smorodinsky-Winternitz system" [20]…”

Section: Introductionmentioning

confidence: 99%

CPN -Rosochatius system, superintegrability, and supersymmetry

2019

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We propose new superintegrable mechanical system on the complex projective space CP N involving a potential term together with coupling to a constant magnetic fields. This system can be viewed as a CP N -analog of both the flat singular oscillator and its spherical analog known as "Rosochatius system". We find its constants of motion and calculate their (highly nonlinear) algebra. We also present its classical and quantum solutions. The system belongs to the class of "Kähler oscillators" admitting SU (2|1) supersymmetric extension. We show that, in the absence of magnetic field and with the special choice of the characteristic parameters, one can construct N = 4, d = 1 Poincaré supersymmetric extension of the system considered. * Electronic address: eivanov@theor.jinr.ru † Electronic address: arnerses@yerphi.am ‡ Electronic address: hovhannes.shmavonyan@mail.yerphi.am

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“…C N -Smorodinsky-Winternitz systemThe C N -Smorodinsky-Winternitz system is defined by the Hamiltonian[16] H SW = N a=1 I a , I a = π aπa + |ω| 2 z aza + |g a | 2 z aza .…”

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confidence: 99%

Symmetries of deformed supersymmetric mechanics on Kähler manifolds

et al. 2020

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Based on the systematic Hamiltonian and superfield approaches we construct the deformed N = 4, 8 supersymmetric mechanics on Kähler manifolds interacting with constant magnetic field, and study their symmetries. At first we construct the deformed N = 4, 8 supersymmetric Landau problem via minimal coupling of standard (undeformed) N = 4, 8 supersymmetric free particle systems on Kähler manifold with constant magnetic field. We show that the initial "flat" supersymmetries are necessarily deformed to SU (2|1) and SU (4|1) supersymmetries, with the magnetic field playing the role of deformation parameter, and that the resulting systems inherit all the kinematical symmetries of the initial ones. Then we construct SU (2|1) supersymmetric Kähler oscillators and find that they include, as particular cases, the harmonic oscillator models on complex Euclidian and complex projective spaces, as well as superintegrable deformations thereof, viz. C N -Smorodinsky-Winternitz and CP N -Rosochatius systems. We show that the supersymmetric extensions proposed inherit all the kinematical symmetries of the initial bosonic models. They also inherit, at least in the case of C N systems, hidden (non-kinematical) symmetries. The superfield formulation of these supersymmetric systems is presented, based on the worldline SU (2|1) and SU (4|1) superspace formalisms. * Electronic address: eivanov@theor.jinr.ru † Electronic address: arnerses@yerphi.am ‡ Electronic address: sidorovstepan88@gmail.com § Electronic address: hovhannes.shmavonyan@yerphi.am the initial kinematical symmetries. However, in the existing literature devoted to supersymmetric extensions of the (generalized) Landau problem, the discussion of symmetry properties of the supersymmetric systems constructed is as a rule left aside (see, e.g., [5,6]).While for N = 2 the construction of such supersymmetric extensions is a rather trivial task, it is not the case for N ≥ 4 supersymmetric extensions. Generically, one may pose the question:How should systems on Kähler manifolds in interaction with a constant magnetic fields (in particular, the Landau problem) be supersymmetrized, so that their initial symmetries be preserved?We guess that the general answer is as follows. Instead of considering N , d = 1 Poincaré supersymmetric extensions of given bosonic systems, one should deal with superextensions based on the proper deformations of standard d = 1 Poincaré supersymmetry.An attempt towards proving this conjecture was performed years ago in [7], where it was observed that the oscillator and the Landau problem on a complex projective space admit the deformed N = 4 supersymmetric extension (later on called "weak N = 4 supersymmetric extension" [8]), which preserves the initial kinematical symmetries of those systems. Departing from this model, the class of systems with non-zero potentials called "Kähler oscillator" was introduced [7,9], such that they admit similar deformed supersymmetric extensions respecting the inclusion of constant magnetic field. The relevant bosonic Hamiltonian...

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CN-Smorodinsky–Winternitz system in a constant magnetic field

Cited by 11 publications

References 43 publications

Quantum SU(2|1) supersymmetric ℂN Smorodinsky-Winternitz system

Quantum SU(2|1) supersymmetric ℂN Smorodinsky-Winternitz system

CPN -Rosochatius system, superintegrability, and supersymmetry

Symmetries of deformed supersymmetric mechanics on Kähler manifolds

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