Deformed Heisenberg algebra and its Hilbert space representations

• URL: http://arxiv.org/abs/2602.15801v1
• Date: Tue, 17 Feb 2026 18:41:30 GMT
• Title: Deformed Heisenberg algebra and its Hilbert space representations
• Authors: Latévi M. Lawson, Ibrahim Nonkané, Kinvi Kangni,
• Abstract summary: A deformation of Heisenberg algebra induces among other consequences a loss of Hermiticity of some operators that generate this algebra.<n>We propose a position deformation of Heisenberg algebra with both maximal length and minimal momentum uncertainties.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: A deformation of Heisenberg algebra induces among other consequences a loss of Hermiticity of some operators that generate this algebra. Therefore, these operators are not Hermitian, nor is the Hamiltonian operator built from them. In the present paper, we propose a position deformation of Heisenberg algebra with both maximal length and minimal momentum uncertainties. By using a pseudo-similarity transformation to the non-Hermitian operators, we prove their Hermiticity with a suitable positive-definite pseudo-metric operator. We then construct Hilbert space representations associated with these pseudo-Hermitian operators. Finally, we study the eigenvalue problem of a free particle in this deformed space and we show that this deformation curved the quantum levels allowing particles to jump from one state to another with low energy transitions.

Related papers

• Uncertainty and Wigner negativity in Hilbert-space classical mechanics [0.0]
  The classical canonical transformations are generated by Hermitian operators that are in general noncommutative.<n>Two hallmark features of quantum mechanics are reproduced, and become apparent, in a Hilbert-space formulation of classical mechanics.
  arXiv  Detail & Related papers  (2026-02-10T22:24:45Z)
• On the Derivation of Equations of Motion from Symmetries in Quantum-Mechanical Systems via Heisenberg's Uncertainty [0.0]
  We construct equations of motion based on symmetries in quantum-mechanical systems.<n>Specific cases are derived -- relativistic, non-relativistic, and a lesser-studied case: ultra-relativistic (Carroll-Schr"odinger)''
  arXiv  Detail & Related papers  (2025-08-14T14:01:08Z)
• Generalization of exact operators of the Foldy-Wouthuysen transformation to arbitrary-spin particles in nonstationary fields [55.2480439325792]
  We use the Foldy-Wouthuysen representation which allows one to obtain the Schr"odinger picture of relativistic quantum mechanics.<n>We determine exact nonexponential and exponential operators of the Foldy-Wouthuysen transformation for arbitrary-spins particles in the nonstationary case.
  arXiv  Detail & Related papers  (2024-10-27T18:41:50Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation [0.0]
  We show that position deformation of a Heisenberg algebra leads to loss of Hermiticity of some operators that generate this algebra.<n>We then construct Hilbert space representations associated with these quasi-Hermitian operators that generate a quasi-Hermitian Heisenberg algebra.<n>We demonstrate that the Euclidean propagator, action, and kinetic energy of this system are constrained by the standard classical mechanics limits.
  arXiv  Detail & Related papers  (2024-04-10T15:11:59Z)
• A non-hermitean momentum operator for the particle in a box [49.1574468325115]
  We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example. The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
  arXiv  Detail & Related papers  (2024-03-20T12:51:58Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Sub-bosonic (deformed) ladder operators [62.997667081978825]
  We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
  arXiv  Detail & Related papers  (2020-09-10T20:53:58Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Covariant Quantum Mechanics and Quantum Spacetime [0.0]
  The basic representation is identified as a coherent state representation, essentially an irreducible component of the regular representation. Explicit wavefunction description is given without any restriction of the variable domains, yet with a finite integral inner product.
  arXiv  Detail & Related papers  (2020-02-04T08:55:56Z)
• Non-commutative graphs in the Fock space over one-particle Hilbert space [0.0]
  We consider examples of the non-commutative operator graphs generated by resolutions of identity corresponding to the Heisenberg-Weyl group of operators acting on the Fock space over one-particle state space. The problem of quantum error correction for such graphs is discussed.
  arXiv  Detail & Related papers  (2019-12-27T13:51:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.