Planar supersymmetric quantum mechanics of a charged particle in an external electromagnetic field

Paschoal, Ricardo C.; Helayël-Neto, J. A.; Assis, Leonardo P. G. De

doi:10.1016/j.physleta.2005.09.016

Cited by 7 publications

(5 citation statements)

References 50 publications

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“…For example, in refs. [32,33], the authors discussed a Lorentz-symmetry violating coupling such that, for a particular background field, eq. ( 2) is recovered upon dimensional reduction.…”

Section: Low-dimensional Systemsmentioning

confidence: 99%

Effective theories and non-minimal couplings in low-dimensional systems

Campos,

Ospedal

2020

Preprint

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Dimensionality aspects of non-minimal electromagnetic couplings are investigated. By means of the Foldy-Wouthuysen transformation, we attain (non-)relativistic interactions related to the non-minimal coupling in three-dimensional spacetime, for both the bosonic and fermionic fields.Next, we establish some comparisons and analyse particular situations in which the external electromagnetic fields are described either by Maxwell or Maxwell-Chern-Simons Electrodynamics. In addition, we consider the situation of a non-minimal coupling for the fermionic field in four dimensions, carry out its dimensional reduction to three dimensions and show that the three-dimensional scenario previously worked out can be recovered as a particular case. Finally, we discuss a number of structural aspects of both procedures.

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“…For example, in refs. [32,33], the authors discussed a Lorentz-symmetry violating coupling such that, for a particular background field, eq. ( 2) is recovered upon dimensional reduction.…”

Section: Low-dimensional Systemsmentioning

confidence: 99%

Effective theories and non-minimal couplings in low-dimensional systems

Campos,

Ospedal

2020

Preprint

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“…Finally, we remember that in N = 2 supersymmetry (without Z), the quiral (φ) and anti-quiral ( φ) superfields have been defined in a manner that satisfy the conditions Dφ = 0 and D φ = 0. By using a Kähler (pre)potential, K(φ, φ), these superfields were applied in the study of supersymmetric models associated with eletromagnetic interaction of a point particle [38,39]. Here, we emphasize that the imposition of the aforementioned conditions with the deformed derivatives leads to a trivial central charge transformations.…”

Section: Supersymmetric Mechanics With Central Chargementioning

confidence: 99%

N=2 Supersymmetry with Central Charge: A Twofold Implementation

Ospedal

Terin

2019

Advances in High Energy Physics

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In this work, we analyze an extended N = 2 supersymmetry with central charge and develop its superspace formulation under two distinct viewpoints. Initially, in the context of classical mechanics, we discuss the introduction of deformed supersymmetric derivatives and their consequence on the deformation of one-dimensional non-linear sigma model. After that, considering a fieldtheoretical framework, we present an implementation of this superalgebra in two dimensions, such that one of the coordinates is related to the central charge. As an application, in this two-dimensional scenario, we consider topological (bosonic) configurations of a special self-coupled matter model and present a non-trivial fermionic solution.

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“…Let us remark that, among other aspects, one of the early works on the Dirac equation dealt with the embedding of different types of supersymmetry (SUSY) [3]. SQM was also explored in a first-order Dirac equation [4] and for the planar electrons [5]. Further, several works exploited supersymmetry to analyze the presence of vector and scalar interactions or the Coulomb potential in it (see, for example, [6,7]).…”

Section: Introductionmentioning

confidence: 99%

Dirac Hamiltonian in a supersymmetric framework

Bagchi,

Ghosh

2021

Preprint

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We investigate the most general form of the one-dimensional Dirac Hamiltonian H D in the presence of scalar and pseudoscalar potentials. To seek embedding of supersymmetry (SUSY) in it, as an alternative procedure to directly employing the intertwining relations, we construct a quasi-Hamiltonian K, defined as the square of H D , to explore the consequences. We show that the diagonal elements of K under a suitable approximation reflects the presence of a superpotential thus proving a useful guide in unveiling the role of SUSY. For illustrative purpose we apply our scheme to the transformed one-dimensional version of the planar electron Hamiltonian under the influence of a magnetic field. We generate spectral solutions for a class of isochronous potentials.

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Planar supersymmetric quantum mechanics of a charged particle in an external electromagnetic field

Cited by 7 publications

References 50 publications

Effective theories and non-minimal couplings in low-dimensional systems

Effective theories and non-minimal couplings in low-dimensional systems

N=2 Supersymmetry with Central Charge: A Twofold Implementation

Dirac Hamiltonian in a supersymmetric framework

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