Classical Dynamics Based on the Minimal Length Uncertainty Principle

Chung, Won Sang

doi:10.1007/s10773-015-2721-0

Cited by 3 publications

(3 citation statements)

References 35 publications

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“…( 8) and ( 9) can reduce to conventional Hamilton equations for the limit f (p) → 1 . Up to the first order inβ , p can be written approximately as [7,10]:…”

Section: Mathematical Formalismmentioning

confidence: 99%

“…The work in this paper is inspired by the generalized uncertainty principle. Some classical problems were already investigated within the framework of deformed Poisson brackets, such as in references [7][8][9][10][11]. In this paper, we study Newtonian gravitation from the classical limit of deformed Heisenberg algebra as proposed by Kempf et al [1].…”

Section: Introductionmentioning

confidence: 99%

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Modified Newton’s gravitational law from deformed Poisson bracket

Siong¹

2019

Turk J Phys

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In this paper, we obtain the modified Newton's gravitational law from deformed Poisson bracket motivated by the generalized uncertainty principle. The modified Newton's gravitational law that we obtain contains a term that plays an important role only in the regime of first order inβ . In the ordinary situation or condition, the modified Newton's gravitational law reduces to the conventional Newton's gravitational law.

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“…( 8) and ( 9) can reduce to conventional Hamilton equations for the limit f (p) → 1 . Up to the first order inβ , p can be written approximately as [7,10]:…”

Section: Mathematical Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modified Newton’s gravitational law from deformed Poisson bracket

Siong¹

2019

Turk J Phys

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“…A number of classical mechanics problem was studied within this scenario [107][108][109][110][111][112][113][114]. Koopman-von Neumann mechanics, however, provides a different and in our opinion more interesting perspective on the Planck scale deformation of classical mechanics.…”

Section: Modification Of Classical Mechanicsmentioning

confidence: 99%

On deformations of classical mechanics due to Planck-scale physics

Chashchina,

Sen,

Silagadze

2019

Preprint

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Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the canonical commutation relations and hence quantum mechanics at the Planck scale. The corresponding modification of classical mechanics is usually considered by replacing modified quantum commutators by Poisson brackets suitably modified in such a way that they retain their main properties (antisymmetry, linearity, Leibniz rule and Jacobi identity). We indicate that there exists an alternative interesting possibility. Koopman-Von Neumann's Hilbert space formulation of classical mechanics allows, as Sudarshan remarked, to consider the classical mechanics as a hidden variable quantum system. Then the Planck scale modification of this quantum system naturally induces the corresponding modification of dynamics in the classical substrate. Interestingly, it seems this induced modification in fact destroys the classicality: classical position and momentum operators cease to be commuting and hidden variables do appear in their evolution equations.

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On deformations of classical mechanics due to Planck-scale physics

Chashchina

Sen

Силагадзе

2020

Int. J. Mod. Phys. D

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Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the canonical commutation relations and hence quantum mechanics at the Planck scale. The corresponding modification of classical mechanics is usually considered by replacing modified quantum commutators by Poisson brackets suitably modified in such a way that they retain their main properties (antisymmetry, linearity, Leibniz rule and Jacobi identity). We indicate that there exists an alternative interesting possibility. Koopman–von Neumann’s Hilbert space formulation of classical mechanics allows, as Sudarshan remarked, to consider the classical mechanics as a hidden variable quantum system. Then, the Planck scale modification of this quantum system naturally induces the corresponding modification of dynamics in the classical substrate. Interestingly, it seems this induced modification in fact destroys the classicality: classical position and momentum operators cease to be commuting and hidden variables do appear in their evolution equations.

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Classical Dynamics Based on the Minimal Length Uncertainty Principle

Cited by 3 publications

References 35 publications

Modified Newton’s gravitational law from deformed Poisson bracket

Modified Newton’s gravitational law from deformed Poisson bracket

On deformations of classical mechanics due to Planck-scale physics

On deformations of classical mechanics due to Planck-scale physics

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