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Cited by 17Algebraic and Geometric AnalysisQuantum and Classical ElectrodynamicsRelativity and Gravitational Theory

Some statistical aspects of the spinor field Fermi-Bose duality

Open access
Simulik, Krivsky, Lamer·2012·Condensed Matter Physics
DOI 10.5488/cmp.15.43101
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Abstract

The structure of 29-dimensional extended real Clifford-Dirac algebra, which has been introduced in our paper Phys.Lett.A, 2011, 375, 2479, is considered in brief.Using this algebra, the property of Fermi-Bose duality of the Dirac equation with nonzero mass is proved.It means that Dirac equation can describe not only the fermionic but also the bosonic states.The proof of our assertion based on the examples of bosonic symmetries, solutions and conservation laws is given.Some statistical aspects of the spinor field Fermi-Bose duality are discussed.

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Crossref · 10.5488/cmp.15.43101

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  • The general form of the FW transformation operator has been obtained in Ref. [42], and in the considered case this operator reduces to [27].

    “The general form of the FW transformation operator has been obtained in Ref. [42]. In the considered case, this operator reduces to [27]”

    From <i>Zitterbewegung</i> of massless particles (2022) · cites this paper as [42]

    Section 3 (equations 6 and 9; page unavailable) gives an explicit Foldy–Wouthuysen transformation operator and shows how it links the FW and Dirac equations. It does not state that this is the general form of the operator or show its reduction to the form cited as [27]. (LLM, conf=0.79)

    Experimental — accuracy not yet measured

  • The FW transformation method gives exact and compact relativistic expressions for all terms proportional to the zero and first powers of the Planck constant and only for such terms proportional to hbar^2 which describe contact interactions, including the Darwin one.

    “However, the FW transformation method [42,44,63,87] applied also in Ref. [27] gives exact and compact relativistic expressions for all terms proportional to the zero and first powers of the Planck constant and only for such terms proportional to ¯ h 2 which describe contact interactions (including the Darwin one).”

    From <i>Zitterbewegung</i> of massless particles (2022) · cites this paper as [42]

    Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

    Experimental — accuracy not yet measured

  • The method of relativistic FW transformation is applicable for a particle in arbitrarily strong external fields, without taking into account effects of quantum field theory.

    “It is applicable for a particle in arbitrarily strong external fields (without taking into account effects of quantum field theory).”

    From <i>Zitterbewegung</i> of massless particles (2022) · cites this paper as [42]

    Section 3 defines the Foldy–Wouthuysen transformation for a Dirac Hamiltonian containing momentum and mass, but does not discuss external fields. Searches for arbitrarily strong external fields and quantum-field-theory effects found no passage addressing the claimed applicability. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

  • The corresponding FW Hamiltonian for a spin-1/2 particle with magnetic and electric dipole moments is given by Eqs. (58)-(60).

    “The corresponding FW Hamiltonian for a spin-1 / 2 particle with magnetic and electric dipole moments (MDM and EDM) is given by [42,88]”

    From <i>Zitterbewegung</i> of massless particles (2022) · cites this paper as [42]

    Section 3 gives a Foldy–Wouthuysen equation linked to the standard Dirac Hamiltonian, while Sections 4–5 discuss Fermi–Bose duality. Searches for magnetic and electric dipole moments and Eqs. (58)–(60) found no passage giving the claimed Hamiltonian; the cited paper’s relevant equations are numbered (7) and (8). Pages were not available in our copy. (LLM, conf=0.77)

    Experimental — accuracy not yet measured

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Cites

Flagged first, then by citations

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  49. Neznamov V.P., Silenko A.J., J. Math. Phys., 2009, 50, 122302; doi:10.1063/1.3268592. Деякi статистичнi аспекти Фермi-Бозе дуалiзму спiнорного поля В.М. Симулик, I.Ю. Кривський, I.Л. Ламер Iнститут електронної фiзики, Нацiональна академiя наук України, вул. Унiверситетська, 21, 88000 Ужгород, Україна Коротко розглядається структура 29-вимiрної розширеної дiйсної алгебри Клiффорда-Дiрака, яка була вве- дена в розгляд у нашiй публiкацiї Phys. Lett. A, 2011, 375, 2479. На основi цiєї алгебри доводиться власти- вiсть Фермi-Бозе дуалiзму рiвняння Дiрака з ненульовою масою. Це означає, що рiвняння Дiрака може описувати не лише фермiоннi, але й бозоннi стани. Доведення дається на прикладах наявностi бозонних симетрiй, розв'язкiв та законiв збереження. Розглянуто деякi статистичнi аспекти Фермi-Бозе дуалiзму спiнорного поля Ключовi слова: спiнорне поле, симетрiя, теоретико-груповий аналiз, суперсиметрiя, представлення Фолдi-Ваутхайзена, алгебра Клiффорда-Дiрака, Фермi-Бозе дуалiзм · DOI

Cited by

Sorted by citations

Authors
Simulik, Krivsky, & Lamer
Affiliations
National Academy of Sciences of Ukraine (UA)
Venue
Condensed Matter Physics
Publisher
Yukhnovskii Institute for Condensed Matter Physics
Published
2012-12
Volume
15
Issue
4
Pages
43101
ISSN
1607-324X (ISSN-L)
DOI
10.5488/cmp.15.43101
OpenAlex
W1617290265
Cited by
17
References
2
Citations by year
2025: 1 · 2023: 2 · 2022: 2 · 2021: 3 · 2020: 1 · 2019: 1 · 2018: 1 · 2017: 1 · 2016: 1 · 2015: 1 · 2014: 2 · 2013: 1
FWCI
2.13
Type
journal article
Language
en
Open access
Locations
  • Condensed Matter Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • The scientific electronic library of periodicals of the National Academy of Sciences of Ukraine (National Academy of Sciences of Ukraine) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Mathematics › Applied Mathematics › Algebraic and Geometric Analysis
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
Keywords
Dirac equation, spinor fields, massive Dirac equation, fermionic states, conservation laws, symmetry

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