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Hilbert space representations for Hermitian position-deformed Heisenberg algebra and path integral formulation.

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Title: Hilbert space representations for Hermitian position-deformed Heisenberg algebra and path integral formulation.
Authors: Katsekpor, Thomas1 (AUTHOR) tkatsekpor@ug.edu.gh, Lawson, Latévi M.1,2,3,4 (AUTHOR) latevi@aims.edu.gh, Osei, Prince K.2,3 (AUTHOR) pkosei@aims.edu.gh, Nonkané, Ibrahim5 (AUTHOR) ibrahim.nonkane@uts.bf
Source: Reviews in Mathematical Physics. May2026, Vol. 38 Issue 4, p1-28. 28p.
Subjects: Hermitian operators, Path integrals, Heisenberg, Werner, 1901-1976, Quantum mechanics, Hilbert space, Similarity transformations, Quantum algebra, Perturbation theory
Abstract: Position deformation of a Heisenberg algebra and Hilbert space representation of both maximal length and minimal momentum uncertainties may lead to loss of Hermiticity of some operators that generate this algebra. Consequently, the Hamiltonian operator constructed from these operators is also not Hermitian. In this paper, with an appropriate positive-definite Dyson map, we establish the Hermiticity of these operators by means of a similarity transformation. We then construct Hilbert space representations associated with these Hermitian operators that generate a Hermitian Heisenberg algebra. With the help of these representations, we establish the path integral formulation of any systems in this Hermitian algebra. Finally, using the path integral of a free particle as an example, we demonstrate that the Euclidean propagator, action, and kinetic energy of this system are constrained by the standard classical mechanics limits. [ABSTRACT FROM AUTHOR]
Copyright of Reviews in Mathematical Physics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Hilbert space representations for Hermitian position-deformed Heisenberg algebra and path integral formulation.
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  Data: <searchLink fieldCode="JN" term="%22Reviews+in+Mathematical+Physics%22">Reviews in Mathematical Physics</searchLink>. May2026, Vol. 38 Issue 4, p1-28. 28p.
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  Data: <searchLink fieldCode="DE" term="%22Hermitian+operators%22">Hermitian operators</searchLink><br /><searchLink fieldCode="DE" term="%22Path+integrals%22">Path integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Heisenberg%2C+Werner%2C+1901-1976%22">Heisenberg, Werner, 1901-1976</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+mechanics%22">Quantum mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Similarity+transformations%22">Similarity transformations</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+algebra%22">Quantum algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Perturbation+theory%22">Perturbation theory</searchLink>
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  Data: Position deformation of a Heisenberg algebra and Hilbert space representation of both maximal length and minimal momentum uncertainties may lead to loss of Hermiticity of some operators that generate this algebra. Consequently, the Hamiltonian operator constructed from these operators is also not Hermitian. In this paper, with an appropriate positive-definite Dyson map, we establish the Hermiticity of these operators by means of a similarity transformation. We then construct Hilbert space representations associated with these Hermitian operators that generate a Hermitian Heisenberg algebra. With the help of these representations, we establish the path integral formulation of any systems in this Hermitian algebra. Finally, using the path integral of a free particle as an example, we demonstrate that the Euclidean propagator, action, and kinetic energy of this system are constrained by the standard classical mechanics limits. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Reviews in Mathematical Physics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1142/S0129055X25500254
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 28
        StartPage: 1
    Subjects:
      – SubjectFull: Hermitian operators
        Type: general
      – SubjectFull: Path integrals
        Type: general
      – SubjectFull: Heisenberg, Werner, 1901-1976
        Type: general
      – SubjectFull: Quantum mechanics
        Type: general
      – SubjectFull: Hilbert space
        Type: general
      – SubjectFull: Similarity transformations
        Type: general
      – SubjectFull: Quantum algebra
        Type: general
      – SubjectFull: Perturbation theory
        Type: general
    Titles:
      – TitleFull: Hilbert space representations for Hermitian position-deformed Heisenberg algebra and path integral formulation.
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            NameFull: Katsekpor, Thomas
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            NameFull: Lawson, Latévi M.
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            NameFull: Osei, Prince K.
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            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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              Value: 38
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            – TitleFull: Reviews in Mathematical Physics
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