The most general form of deformation of the Heisenberg algebra from the generalized uncertainty principle

2016/10/24 by Syed Masood, Mir Faizal, Zaid Zaz +5 · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Black Holes and Theoretical Physics #Classical mechanics #Deformation (meteorology) #Discretization #Harmonic oscillator #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Operator (biology) #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum harmonic oscillator #Quantum mechanics #Uncertainty principle #hep-th

paper · pdf · doi:10.1016/j.physletb.2016.10.047

published as Phys.Lett. B763 (2016) 218-227 · 25 pages, no figures. Accepted for publication in Phys. Lett. B

openalex publication_date 2016/10/24 · arxiv created 2016/10/29 · arxiv updated 2016/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.

Citations

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Cited by

• RGUP Corrections to Scalar and Fermionic Fields