On the Electron Spin Origin and Related Symmetry Aspects
Main Article Content
Abstract
put into the background the algebraic description of the corresponding physically observed representations. There is analyzed in detail, the spin structure and its crucial
dependence on the SU(2)− symmetry properties of the related representations of the basic Clifford algebra, generated by creation-annihilation operators on the Fock space
and the related chirality symmetry of the Pauli spin operators. Based on the conservation law of the spin projection on the electron momentum, a novel derivation of the
Dirac Hamiltonian operator, whose Lorentz invariance is naturally related to that of the fundamental Maxwell equations, whose quanta are carriers of interaction between
electrons.
Downloads
Article Details
Copyright (c) 2026 Prykarpatski AK. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

This work is licensed under a Creative Commons Attribution 4.0 International License.
Minkowski H. Raum und Zeit. Physikalische Zeitschrift. 1909;10:104. Available from: https://www.scirp.org/reference/referencespapers?referenceid=2592037
Weyl H. Group theory and quantum mechanics. 1986.
Dirac PAM. The principles of quantum mechanics. Clarendon Press; 1947. Available from: https://digbib.bibliothek.kit.edu/volltexte/wasbleibt/57355817/57355817.pdf
Pauli W. Theory of Relativity. Oxford; 1958. Available from: https://www.scirp.org/reference/referencespapers?referenceid=1132858
Poincare H. Sur la dynamique de l’electron. Comptes Rendus de l’Academie des Sciences (Paris). 1905;140:1504-1508. Available from: https://www.scirp.org/reference/referencespapers?referenceid=2829094
Baaquie BE. The Theoretical Foundations of Quantum Mechanics. Springer; 2013. Available from: https://link.springer.com/book/10.1007/978-1-4614-6224-8
Blaszak M. Quantum versus Classical Mechanics and Integrability Problems. Springer; 2019. Available from: https://doi.org/10.1007/978-3-030-183790?urlappend=%3Futm_source%3Dresearchgate.net%26utm_medium%3Darticle
Bogolubov NN, Shirkov DV. Quantum Fields. Addison-Wesley; 1982. Available from: https://www.scirp.org/reference/referencespapers?referenceid=1132827
Dong SH, Ma ZQ. Exact solutions to the Dirac equation with a Coulomb potential in 2 + 1 dimensions. Physics Letters A. 2003;312:78-83. Available from: https://doi.org/10.1016/S0375-9601(03)00606-6
Kumar A. Fundamentals of quantum mechanics. Cambridge University Press; 2018. Available from: https://www.cambridge.org/core/books/fundamentals-ofquantum-mechanics/CE1CC368F51875C7E2E995FFF5A9102D
Peskin ME, Schroeder DV. Introduction to quantum fi eld theory. Perseus Books; 1995. Available from: https://www.physicsbook.ir/book/An%20Introduction%20To%20 Quantum%20Field%20Theory%20-%20M.%20Peskin,%20D.%20Schroeder%20(Perseus,%201995).pdf
Radovanovic V. Problem book: quantum fi eld theory. Springer; 2006. Available from: https://emineter.wordpress.com/wp-content/uploads/2015/10/voja-zbirka-qft.pdf
Rebenko AI. Theory of interacting quantum fi elds. De Gruyter; 2010. Available from: https://doi.org/10.1515/9783110250633
Takhtajan LA. Lectures on quantum mechanics. Stony Brook University; Available from: https://www.math.stonybrook.edu/~leontak/570-S06/Lectures.pdf
Jammer M. Concepts of Mass in Contemporary Physics and Philosophy. Princeton University Press; 2009. Available from: https://press.princeton.edu/books/paperback/9780691144320/concepts-of-mass-in-contemporary-physics-and-philosophy?srsltid=AfmBOooJu4W4z50UiHI5esBP1s_qmhSHXqnmVH1NUlFQT0Nr1PeSZuE
Pegg DT. Absorber theory of radiation. Reports on Progress in Physics. 1975;38:1339-1383. Available from: https://inis.iaea.org/records/nt1g0-ep248
Puthoff HE. Casimir vacuum energy and the semiclassical electron. International Journal of Theoretical Physics. 2007;46:3005-3008. Available from: https://arxiv.org/abs/physics/0610042
Simulik VM. The electron as a system of classical electromagnetic and scalar fi elds. In: Simulik VM, editor. What is the electron? Montreal: Apeiron; p.109-134.
Wheeler JB, Feynman RP. Interaction with the absorber as the mechanism of radiation. Reviews of Modern Physics. 1945;17(2-3):157-181. Available from: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.17.157
Yaremko Y, Tretyak V. Radiation reaction in classical fi eld theory. LAP LAMBERT Academic Publishing; 2012. Available from: https://doi.org/10.48550/ arXiv.1207.5148
Feynman R, Leighton R, Sands M. The Feynman Lectures on Physics. Vol. 2, Electrodynamics. Addison-Wesley; 1964. Available from: https://mathphyche.wordpress.com/wp-content/uploads/2020/01/the-feynman-lectures-on-physics-vol.-ii_-the-new-millennium-edition_-mainly-electromagnetism-and-matter.pdf
Feynman R, Leighton R, Sands M. The Feynman Lectures on Physics. Vol. 1, Mechanics, space, time and motion. Addison-Wesley; 1963. Available from: https://www.feynmanlectures.caltech.edu/
Hammond RT. Electrodynamics and radiation reaction. Foundations of Physics. 2013;43:201-209. Available from: https://doi.org/10.1007/s10701-012-9687-z
Hammond RT. Relativistic particle motion and radiation reaction. Electronic Journal of Theoretical Physics. 2010;(23):221-258. Available from: https://www.aldebaran.cz/ts/docs_re/2010_Hammond.pdf
Kosyakov BP. Radiation in electrodynamics and in Yang-Mills theory. Soviet Physics Uspekhi. 1992;35(2):135-142. Available from: https://ufn.ru/en/articles/1992/2/e/
Kosyakov BP. Introduction to the classical theory of particles and fi elds. Springer; 2007. Available from: https://ndl.ethernet.edu.et/bitstream/123456789/32975/1/1.pdf.pdf
Brillouin L. Relativity reexamined. Academic Press; 1970. Available from: https://www.scirp.org/reference/referencespapers?referenceid=96887
Gill TL, Zachary WW. Two mathematically equivalent versions of Maxwell equations. Preprint. 2008. Available from: https://doi.org/10.48550/arXiv.1009.3068
Gill TL, Zachary WW. Two mathematically equivalent versions of Maxwell’s equations. Foundations of Physics. 2011;4:99-128. Available from: https://link.springer.com/article/10.1007/s10701-009-9331-8
Prykarpatski AK. Classical electromagnetic theory revisiting: The A.M. Ampere law and the vacuum fi eld theory approach. Universal Journal of Physics and Application. 2014;2(8):381-413. Available from: https://doi.org/10.13189/ujpa.2014.020804
Martins AA, Pinheiro MJ. On the electromagnetic origin of inertia and inertial mass. International Journal of Theoretical Physics. 2008;47:2706-2715. Available from: https://link.springer.com/article/10.1007/s10773-008-9709-y
Medina R. Radiation reaction of a classical quasi-rigid extended particle. Journal of Physics A: Mathematical and General. 2006:3801-3816. Available from: https://doi.org/10.48550/arXiv.physics/0508031
Morozov VB. On the question of the electromagnetic momentum of a charged body. Physics Uspekhi. 2011;181(4):389-392. Available from: https://doi.org/10.48550/arXiv.2007.03468
Page L, Adams NI Jr. Action and reaction between moving charges. American Journal of Physics. 1945;13:141-147. Available from: https://doi.org/10.1119/1.1990689
Pappas PT. The original Ampere force and Biot-Savart and Lorentz force. Il Nuovo Cimento B. 1983;76(2):189-197. Available from: https://link.springer.com/article/10.1007/BF02721552
Annila A. The Meaning of Mass. International Journal of Theoretical and Mathematical Physics. 2012;2(4):67-78. Available from: http://article.sapub.org/10.5923.j.ijtmp.20120204.03.html
Higgs P. Broken symmetries and the masses of gauge bosons. Physical Review Letters. 1964;13:508. Spontaneous symmetry breakdown without massless bosons. Physical Review. 1964;145:1156. Available from: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.13.508
t’Hooft G. Massive Yang-Mills fi elds. Nuclear Physics B. 1971;35:167. Available from: https://inspirehep.net/literature/67962
Wilczek F. QCD and natural philosophy. Annales Henri Poincare. 2003;4:211-228. Available from: https://link.springer.com/article/10.1007/s00023-003-0917-y40. Wilczek F. Origins of mass. 2012. Available from: https://arxiv.org/abs/1206.7114
Fock V. Die Eigenzeit in der klassischen und in der Quantenmechanik. Sow Physics. 1937;12:404-425. Available from: https://www.neo-classical-physics.info/uploads/3/4/3/6/34363841/fock_-_wkb_and_dirac.pdf
Coddens G. The geometrical meaning of spinors as a key to make sense of quantum mechanics. 2021. Available from: https://hal.science/hal-03175981/document
Prykarpatski AK. On the electron spin and spectrum energy problems within the Fock many temporal and Feynman proper time paradigms. Journal of Physics: Conference Series. 2023;2482:012017. Available from: https://iopscience.iop.org/article/10.1088/1742-6596/2482/1/012017
Blackmore D, Prykarpatsky AK, Samoylenko VHr. Nonlinear dynamical systems of mathematical physics: spectral and differential-geometrical integrability analysis. World Scientifi c Publ.; 2011. Available from: https://researchwith.njit.edu/en/publications/nonlinear-dynamical-systems-of-mathematical-physics-spectral-and-/
Bogolubov NN, Logunov AA, Oksak AI, Todorov IT. General Principles of Quantum Field Theory. Kluwer; 1990. Available from: https://inspirehep.net/literature/2745560
Bogolubov NN Jr, Prykarpatsky AK, Blackmore D. Maxwell–Lorentz Electrodynamics Revisited via the Lagrangian Formalism and Feynman Proper Time Paradigm. Mathematics. 2015;3:190-257. Available from: https://www.mdpi.com/2227-7390/3/2/190
Dirac PAM, Fock VA, Podolsky B. On quantum electrodynamics. Sow Physics. 1932;2:468-479.
Dyson FJ. Feynman’s proof of the Maxwell equations. American Journal of Physics. 1990;58:209-211. Available from: https://scispace.com/pdf/feynman-s-proof-ofthe-maxwell-equations-47n22g6hxp.pdf
Dyson FJ. Feynman at Cornell. Physics Today. 1989;42(2):32-38. Available from: https://doi.org/10.1063/1.881190
Fock VA, Podolsky B. On the quantization of electromagnetic waves and the interaction of charges in Dirac’s theory. Sow Physics. 1932;1:801-817.
Prykarpatsky AK, Bogolubov NN Jr. On the classical Maxwell-Lorentz electrodynamics, the electron inertia problem, and the Feynman proper time paradigm. Ukrainian Journal of Physics. 2016;61(3):187-212. Available from: https://arxiv.org/abs/1412.8646