Reducibility and Bosonization of Parasupersymmetric and Orthosupersymmetric Quantum Mechanics

Quesne, Christiane; Vansteenkiste, Nicolas

doi:10.1142/s021773230200717x

Cited by 8 publications

(8 citation statements)

References 26 publications

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“…(1) and (2) by considering occupancy of neutron h 11/2 orbital. As in the reference [44], it was shown that the interactions of order higher than 2 are important in the 0f 7/2 shell for f p shell nuclei. In our case for Te isotopes, with 2 protons outside Z = 50 core, there is no contribution of three-body…”

Section: Estimate For Contributions From Three-body Forcessupporting

confidence: 53%

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Analysis of proton and neutron pair breakings: High-spin structures of 124–127 Te isotopes

et al. 2015

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In the present work recently available experimental data for high-spin states of four nuclei, 124 52 Te, 125 52 Te, 126 52 Te, and 127 52 Te, have been interpreted using state-of-the-art shell model calculations. The calculations have been performed in the 50-82 valence shell composed of 1g 7/2 , 2d 5/2 , 1h 11/2 , 3s 1/2 , and 2d 3/2 orbitals. We have compared our results with the available experimental data for excitation energies and transition probabilities, including high-spin states. The results are in reasonable agreement with the available experimental data. The wave functions, particularly, the specific proton and neutron configurations which are involved to generate the angular momentum along the yrast lines are discussed. We have also estimated overall contribution of three-body forces in the energy level shifting. Finally, results with modified effective interaction are also reported.

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Section: Estimate For Contributions From Three-body Forcessupporting

confidence: 53%

“…It may also shift the individual states different way. The importance of three-body forces for lighter nuclei were reported in literature [44,45,46,47,48]. The average energy shift of states with n valence particles due to a 3N force can be written as…”

Section: Estimate For Contributions From Three-body Forcesmentioning

confidence: 98%

Analysis of proton and neutron pair breakings: High-spin structures of 124–127 Te isotopes

et al. 2015

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“…The two corresponding eigenspaces F 0 and F 1 , made of even or odd number states, respectively, are such that F = F 0 ⊕ F 1 , the corresponding projectors being P 0 = 1 2 (1 + T ) and P 1 = 1 2 (1 − T ). On starting from the general results obtained for order-p parasupersymmetric quantum mechanics in [24] and setting p = 1, which gives back SUSYQM, we arrive at two different realizations of superalgebra (15) in terms of the GDOA (27), namely…”

Section: Bosonization In Terms Of a Gdoamentioning

confidence: 99%

“…In such a framework, SUSYQM turns out to be fully reducible, its irreducible components providing two sets of bosonized operators realizing either broken or unbroken SUSYQM. Such an approach in terms of GDOAs was latter on applied [24,25,26] to several variants of SUSYQM, namely parasupersymmetric [27,28,29], orthosupersymmetric [30], pseudosupersymmetric [31], and fractional supersymmetric quantum mechanics [32].…”

Section: Introductionmentioning

confidence: 99%

Minimal bosonization of double-graded supersymmetric quantum mechanics

Quesne

2021

Preprint

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The superalgebra of Z 2 2 -graded supersymmetric quantum mechanics is shown to be realizable in terms of a single bosonic degree of freedom. Such an approach is directly inspired by a description of the corresponding Z 2 -graded superalgebra in the framework of a Calogero-Vasiliev algebra or, more generally, of a generalized deformed oscillator algebra. In the case of the Z 2 2 -graded superalgebra, the central element Z has the property of distinguishing between degenerate eigenstates of the Hamiltonian.

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“…In the q‐deformed theory we have a famous q‐deformed exponential functions called Jackson's q‐exponential function which is defined by

0true e_{q}^{J} (x) = \sum_{n = 0}^{\infty} \frac{1}{false[n false]!} x^{n}

where q‐number is defined as

{[n]}_{q} = \frac{q^{n} - 1}{q - 1}

The Jackson's q‐exponential function obeys

\partial_{x}^{q} e_{q}^{J} false(x false) = e_{q}^{J} false(x false)

where Jackson's q‐derivative was defined as

\partial_{x}^{q} F false(x false) = \frac{F (q x) - F (x)}{x (q - 1)}

Acting the Jackson's q‐derivative on monomials yields

\partial_{x}^{q} x^{n} = {[n]}_{q} x^{n - 1}

The Jackson's q‐derivative was used in the study of q‐deformed bosonic system and several investigators have studied the equilibrium statistical mechanics of the gas of non‐interacting q‐boson systems …”

Section: Introductionmentioning

confidence: 99%

q‐Deformed Quantum Mechanics Based on the q‐Addition

Chung

Hassanabadi

2019

Fortschritte der Physik

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In this paper we consider the q‐derivative appearing in the non‐extensive thermodynamics to formulate the q‐deformed quantum mechanics. From the q‐addition we discuss the q‐deformed calculus and q‐deformed elementary functions. We use these to construct the q‐deformed quantum mechanics. As examples we discuss momentum eigenfunction, one dimensional box problem and quantum harmonic potential problem.

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Reducibility and Bosonization of Parasupersymmetric and Orthosupersymmetric Quantum Mechanics

Cited by 8 publications

References 26 publications

Analysis of proton and neutron pair breakings: High-spin structures of 124–127 Te isotopes

Analysis of proton and neutron pair breakings: High-spin structures of 124–127 Te isotopes

Minimal bosonization of double-graded supersymmetric quantum mechanics

q‐Deformed Quantum Mechanics Based on the q‐Addition

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