On Duffin–Kemmer–Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound-states for the one-dimensional inversely linear background

Castro, Antonio S. de

doi:10.1063/1.3494292

Cited by 9 publications

(5 citation statements)

References 36 publications

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“…We illustrate this equivalence by explicitly building the lowest dimensional (irreducible) representation of the theory. At the end we comment how our result explain why several authors in recent years found identical results for both the spin-0 and spin-1 sectors of the (3+1) dimensional DKP equation when the dynamics is restricted to only one space dimension [10][11][12][13][14][15][16][17][18][19][20] .…”

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confidence: 64%

A note on the Duffin-Kemmer-Petiau equation in (1+1) space-time dimensions

Lunardi

2017

Journal of Mathematical Physics

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In the last years several papers addressed the supposed spin-1 sector of the massive Duffin-Kemmer-Petiau (DKP) equation restricted to (1+1) space-time dimensions. In this note we show explicitly that this is a misleading approach, since the DKP algebra in (1+1) dimensions admits only a spin-0 representation. Our result also is useful to understand why several recent papers found coincident results for both spin-0 and spin-1 sectors of the DKP theory in (3+1) dimensions when the dynamics is restricted to one space dimension.The Duffin-Kemmer-Petiau (DKP) equation is a first order wave equation similar to the Dirac one, which in its original formulation in (3+1) space-time dimensions describes spin-0 and spin-1 fields or particles 1-5 . In recent years some papers addressed the DKP equation in strict (1+1) space-time dimensions in situations involving interactions and addressed the supposed spin-1 sector of the theory 6-9 . In this note we show explicitly that such an approach is misleading; by using the (1+1)-dimensional analogs of the original DKP spin-0 and spin-1 projection operators we show that the supposed "spin-1" sector of the theory restricted to (1+1) dimensions actually is unitarily equivalent to its spin-0 sector, which describes a (pseudo)scalar field. We illustrate this equivalence by explicitly building the lowest dimensional (irreducible) representation of the theory. At the end we comment how our result explain why several authors in recent years found identical results for both the spin-0 and spin-1 sectors of the (3+1) dimensional DKP equation when the dynamics is restricted to only one space dimension 10-20 .DKP equation in (3+1) dimensions. We start by recalling some basic results about the free DKP equation in (3+1) space-time dimensions. The equation is given by 1-5 (we use natural units = c = 1)where m is the particle's mass, ψ is the DKP wave function and β µ are matrices satisfying the DKP algebrawhere g µν is the Minkowski metric tensor in (3+1) dimensions with signature (+, −, −, −).It is well known that there are only three irreducible representations (irrep's) of DKP algebra in (3+1) dimensions: one is trivial, having dimension 1, and the other two are nontrivial, having dimensions 5 and 10, corresponding respectively to scalar (spin-0) and vector (spin-1) fields 4,21,22 . Under infinitesimal Lorentz transformations x ′µ = Λ µ ν x ν , with Λ µν = g µν + ω µν , ω µν = −ω νµ , the DKP spinor ψ transforms as ψ → U ψ, where 5 U = 1 + 1 2 ω µν S µν , S µν = [β µ , β ν ] .

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confidence: 64%

A note on the Duffin-Kemmer-Petiau equation in (1+1) space-time dimensions

Lunardi

2017

Journal of Mathematical Physics

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“…From Eqs. ( 22), (23), and (29) we find H +1 , H −1 , G 0 in terms of F 0 . Then, we employ them in Eq.…”

Section: A (−1) J Parity Statessupporting

confidence: 54%

“…Then, by using the properties of vector spherical harmonics [2,7,23], we obtain the following radial differential equations:…”

Section: Dkp Equation In the Presence Of Minimum Uncertainty In Momentummentioning

confidence: 99%

“…If the nonminimal vector potential is invariant under charge conjugation, then, one can not discriminate the particle from its antiparticle [20]. Since the DKPe, unlike from KG and Proca equations, allows the nonminimal couplings, it is extensively examined by considering several Lorentz structures [2,7,15,23,51,53], and potential energies [6,37,38,40,58,59].…”

Section: Introductionmentioning

confidence: 99%

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The spin-one DKP Equation with a nonminimal vector interaction in the presence of minimal uncertainty in momentum

Hamil,

Lütfüoğlu,

Aounallah

2021

Preprint

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In this work, we consider the relativistic Duffin-Kemmer-Petiau equation for spin-one particles with a nonminimal vector interaction in the presence of minimal uncertainty in momentum. By using the position space representation we exactly determine the bound-states spectrum and the corresponding eigenfunctions. We discuss the effects of the deformation and nonminimal vector coupling parameters on the energy spectrum analytically and numerically.

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“…Among the potentials used, we can highlight the double-step potential [16,17], the DKP oscillator [18,19], the inversely linear background [20], the mixed minimal-nonminimal vector cusp potential [21].…”

Section: Introductionmentioning

confidence: 99%

Quantum dynamics of relativistic bosons through nonminimal vector square potentials

Oliveira

2016

Annals of Physics

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The dynamics of relativistic bosons (scalar and vectorial) through nonminimal vector square (well and barrier) potentials is studied in the Duffin-Kemmer-Petiau (DKP) formalism. We show that the problem can be mapped in effective Schrödinger equations for a component of the DKP spinor. An oscillatory transmission coefficient is found and there is total reflection. Additionally, the energy spectrum of bound states is obtained and reveals the Schiff-Snyder-Weinberg effect, for specific conditions the potential lodges bound states of particles and antiparticles.

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On Duffin–Kemmer–Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound-states for the one-dimensional inversely linear background

Cited by 9 publications

References 36 publications

A note on the Duffin-Kemmer-Petiau equation in (1+1) space-time dimensions

A note on the Duffin-Kemmer-Petiau equation in (1+1) space-time dimensions

The spin-one DKP Equation with a nonminimal vector interaction in the presence of minimal uncertainty in momentum

Quantum dynamics of relativistic bosons through nonminimal vector square potentials

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