Position and spin in relativistic quantum mechanics
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The problem of the position and spin in relativistic quantum mechanics is analyzed in detail. It is definitively shown that the position and spin operators in the Foldy-Wouthuysen representation (but not in the Dirac one) are quantum-mechanical counterparts of the classical position and spin variables. The probabilistic interpretation is valid only for Foldy-Wouthuysen wave functions. The relativistic spin operators are discussed. The spin-orbit interaction does not exist for a free particle if the conventional operators of the orbital angular momentum and the rest-frame spin are used. Alternative definitions of the orbital angular momentum and the spin are based on noncommutative geometry, do not satisfy standard commutation relations, and can allow the spin-orbit interaction.
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In the Foldy-Wouthuysen representation, Zitterbewegung disappears for massless Dirac particles.
“In the FW representation, it disappears not only for massive [9-11] but also for massless Dirac particles.”
From <i>Zitterbewegung</i> of massless particles (2022) · cites this paper as [11]
This conclusion agrees with previous studies [3-5,9-14] for massive particles.
“This is the same conclusion which has been made in the previous studies [3-5,9-14].”
From <i>Zitterbewegung</i> of massless particles (2022) · cites this paper as [11]
The citing sentence does not identify what “this conclusion” is, so its agreement with the cited paper cannot be assessed. Section B (pp. 31–32) discusses conclusions about spin-orbit interaction and the distinction between massive and massless particles, but the sentence provides no antecedent that would establish which conclusion it attributes to this source. (LLM, conf=0.68)
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References 165 · Cited by 45
Research works printed but not linked: 13
- [1]M. H. L. Pryce, The mass-centre in the restricted theory of relativity and its connexion with the quantum theory of elementary particles, Proc. R. Soc. London A 195 , 62 (1948).
- [28]M. Reiher and A. Wolf, Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science (Wiley-VCH, Weinheim, 2009).
- [39]V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitayevskii, Quantum Electrodynamics , 2nd ed. (Pergamon, Oxford, 1982).
- [60]I. Kirsch, L. H. Ryder and F. W. Hehl, The Gordon decompositions of the inertial currents of the Dirac electron correspond to a Foldy-Wouthuysen transformation, arXiv:hep-th/0102102 (2001). · arXiv
- [71]A.J. Silenko, Classical and quantum spins in curved spacetimes, Acta Phys. Polon. B Proc. Suppl. 1 , 87 (2008).
- [76]Yu. N. Obukhov, A. J. Silenko, and O. V. Teryaev, Spin-Gravity Interactions and Equivalence Principle, Int. J. Mod. Phys.: Conf. Ser. 40 , 1660081 (2016).
- [81]V.M. Simulik, I. Yu. Krivsky, On the extended real Clifford-Dirac algebra and new physically meaningful symmetries of the Dirac equations with nonzero mass, Reports of the National Academy of Sciences of Ukraine, No. 5, 82 (2010).
- [84]V.M. Simulik, I. Yu. Krivsky, I. L. Lamer, Bosonic symmetries, solutions, and conservation laws for the Dirac equation with nonzero mass, Ukrainian Journal of Physics 58 , 523 (2013).
- [103]E. D. Commins and P. H. Bucksbaum, Weak Interactions of Leptons and Quarks (Cambridge Univ. Press, Cambridge, 1983).
- [113]V. Bargmann and E. P. Wigner, Group Theoretical Discussion of Relativistic Wave Equations, Proc. Natl. Acad. Sci. U.S.A. 34 , 211 (1948).
- Wheeler , edited by I. Ciufolini and R. Matzner (Springer, Berlin, 2010).
- [126]M. E. Rose, Relativistic Electron Theory (Wiley, New York, 1961).
- [127]J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964), p. 52.
- Authors
- Zou, L., Zhang, P., & Silenko, A. J.
- Affiliations
- Chinese Academy of Sciences (CN)
- Sun Yat-sen University (CN)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2020-03-26
- Volume
- 101
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W3011328850
- Cited by
- 45
- References
- 165
- Citations by year
- 2026: 3 · 2025: 7 · 2024: 7 · 2023: 12 · 2022: 7 · 2021: 6 · 2020: 3
- FWCI
- 2.85
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Digital Library of the Belarusian State University (Belarusian State University) (submittedVersion, cc-by)
- arXiv (Cornell University)
- Funders
- Belarusian Republican Foundation for Fundamental Research (18D-002)
- National Natural Science Foundation of China (11975320, 11805242)
- Chinese Academy of Sciences (2019VMA0019)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- 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
- relativistic quantum mechanics, Foldy-Wouthuysen representation, Dirac equation, position operator, spin operators, relativistic spin, spin-orbit coupling, orbital angular momentum, noncommutative geometry, probabilistic interpretation, free particle
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