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-Rosochatius system, superintegrability, and supersymmetry

Ivanov, E.; Nersessian, Armen; Shmavonyan, Hovhannes

doi:10.1103/physrevd.99.085007

Cited by 7 publications

(13 citation statements)

References 73 publications

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“…It is interesting that, in contrast to C N -Smorodinsky-Winternitz system, in the absence of magnetic field and under the special choice of the parameters ω i , this system admits flat N = 4, d = 1 "Poincaré" supersymmetry [18]. The choice just mentioned is as follows…”

Section: B Complex Projective Spacesmentioning

confidence: 99%

“…It is more or less obvious that the inclusion of constant fields preserves the initial symmetries of the free particle moving on the generic Kähler manifold as well, and (spinless) Landau problem can be defined for any Kähler manifold. In order to restore the initial meaning of the Landau problem in the context of these systems one should try to construct supersymmetric extensions of the (spinless) Landau problem on Kähler manifold, such that they preserve • CP N -Rosochatius system [18], i.e. the CP N -counterpart of C N -Smorodinsky-Winternitz system.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: B Complex Projective Spacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symmetries of deformed supersymmetric mechanics on Kähler manifolds

et al. 2020

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“…Replacing H byȧ/a and multiplying across by a 3 yields (d/dt)(ρa 3 ) + (p + P )(d/dt)a 3 = 0 or dU + (p + P )dV = 0 -exactly as (4), if one identifies the pressure P in (8) with the creation-entropy pressure (6). In other words, the reason for absorbing the entropy and particle creation terms from (3) into the new pressure term P is to match the second law of thermodynamics (3) with dU + (p + P )dV = 0, which follows from the energy conservation equatioṅ ρ = −3H(ρ + p + P ).…”

Section: The Model With Non-conserved Specific Entropymentioning

confidence: 99%

“…However, there are no equations from which the form of Γ can be determined. The consensus [1,2,3,4,5,6] is that Γ should be considered as an input characteristic in the phenomenological description. In this paper the Universe is modelled as a perfect fluid comprising of an ideal monoatomic gas containing a single type of particles with non-conserved number.…”

Section: Introductionmentioning

confidence: 99%

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On the cosmological models with matter creation

Ivanov

Prodanov

2019

Eur. Phys. J. C

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The matter creation model of Prigogine-Géhéniau-Gunzig-Nardone is revisited in terms of a redefined creation pressure which does not lead to irreversible adiabatic evolution at constant specific entropy. With the resulting freedom to choose a particular gas process, a flat FRWL cosmological model is proposed based on three input characteristics: (i) a perfect fluid comprising of an ideal gas, (ii) a quasi-adiabatic polytropic process, and (iii) a particular rate of particle creation. Such model leads to the description of the late-time acceleration of the expanding Universe with a natural transition from decelerating to accelerating regime. Only the Friedmann equations and the laws of thermodynamics are used and no assumptions of dark energy component is made. The model also allows the explicit determination as functions of time of all variables, including the entropy, the non-conserved specific entropy and the time the accelerating phase begins. A form of correspondence with the dark energy models (quintessence, in particular) is established via the Om diagnostics. Parallels with the concordance cosmological ΛCDM model for the matter-dominated epoch and the present epoch of accelerated expansion are also established via slight modifications of both models.

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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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CPN -Rosochatius system, superintegrability, and supersymmetry

Cited by 7 publications

References 73 publications

Symmetries of deformed supersymmetric mechanics on Kähler manifolds

Symmetries of deformed supersymmetric mechanics on Kähler manifolds

On the cosmological models with matter creation

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

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