Generalized uncertainty principle, extra-dimensions and holography

Scardigli, Fabio; Casadio, Roberto

doi:10.1590/s0103-97332005000300017

Cited by 12 publications

(12 citation statements)

References 20 publications

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“…This latter implies a minimal position uncertainty ∆x min [4,5,6,7,8]. Moreover, the emergence of this minimal length in non-relativistics quantum mechanics introduces many consequences such as the deformation of the Heisenberg algebra, the loss of the localization of particles in the position representation, the deformation of the structures of the Hilbert space, the noncommutation in position space [4] etc.…”

Section: Introductionmentioning

confidence: 99%

Minimal and maximal lengths from position-dependent non-commutativity

Lawson¹

2020

J. Phys. A: Math. Theor.

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Fring et al. in Ref.[1] have introduced a new set of noncommutative space-time commutation relations in two space dimensions. It had been shown that any fundamental objects introduced in this space-space noncommutativity are string-like. Taking this result into account, we generalize the seminal work of Fring et al to the case that there is also a maximal length from position-dependent noncommutativity and a minimal momentum arising from generalized versions of Heisenberg's uncertainty relations. The existence of maximal length is related to the presence of an extra, first order term in particle's length that provides the basic difference of our analysis with theirs. This maximal length breaks up the well known singularity problem of space time. We establish different representations of this noncommutative space and finally we study some basic and interesting quantum mechanical systems in these new variables.

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Section: Introductionmentioning

confidence: 99%

Minimal and maximal lengths from position-dependent non-commutativity

Lawson¹

2020

J. Phys. A: Math. Theor.

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“…According to this, the development of mathematical manipulation to handle the minimal length became a central issue in modern quantum gravity. The several research fields in which the concept of an observable minimal length plays an important role in their complete description are string theory [1][2][3][4][5], loop quantum gravity [6], noncommutative geometry [7], noncommutative field theories [8][9][10], and black-hole physics [11,12]. Standard formulation of quantum mechanics with minimal length for these systems has been carried out starting from the modified Heisenberg algebra with a deformed commutation relation between position and momentum operators, which arises from intrinsic noncommutativity in geometries [13,14].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Dirac Oscillator with Minimal Length: Novel Phenomena for Quantized Energy

Betrouche

Maamache

Choi

2013

Advances in High Energy Physics

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We study quantum features of the Dirac oscillator under the condition that the position and the momentum operators obey generalized commutationrelations that lead to the appearance of minimal length with the order of the Planck length,∆xmin=ℏ3β+β′, whereβandβ′are two positive small parameters. Wave functions of the system and the corresponding energy spectrum are derived rigorously. The presence of the minimal length accompanies a quadratic dependence of the energy spectrum on quantum numbern, implying the property of hard confinement of the system. It is shown that the infinite degeneracy of energy levels appearing in the usual Dirac oscillator is vanished by the presence of the minimal length so long asβ≠0. Not only in the nonrelativistic limit but also in the limit of the standard case(β=β′=0), our results reduce to well known usual ones.

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“…On the other hand, various researches regarding the quantum gravity [3,68] and cosmology [10], string theory [64,65], noncommutative geometry [54], black hole physics [70] and thermodynamics [63] show that a minimal observable length should exist.This minimal length (ML) may be introduced as an additional uncertainty in position measurements ∆x min , which leads to a generalization of Heisenberg's uncertainty principle. Kempf with his collaborators [41,[47][48][49], showed that a ML can be obtained out of the generalized Heisenberg algebra with the form…”

Section: Introductionmentioning

confidence: 99%

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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Generalized uncertainty principle, extra-dimensions and holography

Cited by 12 publications

References 20 publications

Minimal and maximal lengths from position-dependent non-commutativity

Minimal and maximal lengths from position-dependent non-commutativity

Three-Dimensional Dirac Oscillator with Minimal Length: Novel Phenomena for Quantized Energy

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

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