The {\cal N}=1 supersymmetric Landau problem and its supersymmetric Landau level projections: the {\cal N}=1 supersymmetric Moyal–Voros superplane

Geloun, Joseph Ben; Govaerts, Jan; Scholtz, F. G.

doi:10.1088/1751-8113/42/49/495203

Cited by 4 publications

(2 citation statements)

References 20 publications

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“…However we still need to investigate the gauge transformation properties of the vector superfield in order to define an invariant action. In the case of a U(1) gauge group [18], the gauge transformation of the vector superfield is V → V − iDΛ where the superfield Λ is real and reads…”

Section: Non-abelian Transformations and Supersymmetric Actionmentioning

confidence: 99%

The $\mathcal{N}=1$ supersymmetric Wong equations and the non-abelian Landau problem

Fanuel¹,

Govaerts²,

Avossevou³

et al. 2014

J. Phys. A: Math. Theor.

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A Lagrangian formulation is given extending to N = 1 supersymmetry the motion of a charged point particle with spin in a non-abelian external field. The classical formulation is constructed for any external static non-abelian SU(N) gauge potential. As an illustration, a specific gauge is fixed enabling canonical quantization and the study of the supersymmetric non-abelian Landau problem. The spectrum of the quantum Hamiltonian operator follows in accordance with the supersymmetric structure.

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Section: Non-abelian Transformations and Supersymmetric Actionmentioning

confidence: 99%

The $\mathcal{N}=1$ supersymmetric Wong equations and the non-abelian Landau problem

Fanuel¹,

Govaerts²,

Avossevou³

et al. 2014

J. Phys. A: Math. Theor.

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“…In commutative case, supersymmetric quantum mechanics is a well developed subject which has led to the understanding of many subtle issues of supersymmetric field theories in a much simpler way. As a matter of fact NC supersymmetric quantum mechanics have also been studied much in the literature in one dimension and higher dimensions [28]- [30]. The aspect of NC U(1) * gauge invariance is an important issue in this context and had been considered in [28].…”

Section: Introductionmentioning

confidence: 99%

Pauli equation on noncommutative plane and the Seiberg–Witten map

Halder¹,

Gangopadhyay

2016

Mod. Phys. Lett. A

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We study the Pauli equation in noncommutative two dimensional plane which exhibits the supersymmetry algebra when the gyro-magnetic ratio is 2. The significance of the Seiberg-Witten map in this context is discussed and its effect in the problem is incorporated to all orders in θ. We map the noncommutative problem to an equivalent commutative problem by using a set of generalised Bopp-shift transformations containing a scaling parameter. The energy spectrum of the noncommutative Pauli Hamiltonian is obtained and found to be θ corrected which is valid to all orders in θ.

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Landau problem with time dependent mass in time dependent electric and harmonic background fields

Lawson

Avossevou

2018

Journal of Mathematical Physics

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The spectrum of a Hamiltonian describing the dynamics of a Landau particle with time-dependent mass and frequency undergoing the influence of a uniform time-dependent electric field is obtained. The configuration space wave function of the model is expressed in terms of the generalised Laguerre polynomials. To diagonalize the time-dependent Hamiltonian, we employ the Lewis-Riesenfeld method of invariants. To this end, we introduce a unitary transformation in the framework of the algebraic formalism to construct the invariant operator of the system and then to obtain the exact solution of the Hamiltonian. We recover the solutions of the ordinary Landau problem in the absence of the electric and harmonic fields for a constant particle mass.

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The {\cal N}=1 supersymmetric Landau problem and its supersymmetric Landau level projections: the {\cal N}=1 supersymmetric Moyal–Voros superplane

Cited by 4 publications

References 20 publications

The $\mathcal{N}=1$ supersymmetric Wong equations and the non-abelian Landau problem

The $\mathcal{N}=1$ supersymmetric Wong equations and the non-abelian Landau problem

Pauli equation on noncommutative plane and the Seiberg–Witten map

Landau problem with time dependent mass in time dependent electric and harmonic background fields

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