ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

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Mathematical IQM Gauge Theory for Interaction Processes

Автор(ы):

Zoran Majkic

International Society for Research in Science and Technology

majk.1234@yahoo.com

Аннотация:

We provide a mathematical development of generalized gauge theory for interactions of an individual particle represented by a complex energy-density wave-packet in the Minkowski time-space. So, we obtained a general gauge 4-potential field which determinates the acceleration of this particle, by using the complex phase transformation of the wave-packet, generated during any interaction process, with local symmetry of the Lagrangian density: the Euler-Lagrange equation derived from this Lagrangian density represents the partial differential equation of motion of thye packet. This developed mathematical theory is then applied for the famous example of the Aharonov-Bohm effect for the electrons.

Ключевые слова

Ссылки:

  1. Ehrenberg W. and Siday R., The Refractive Index in Electron Optics and the Principles of Dynamics, Proceedings of the Physical Society, Series B, 62, 1949
  2. Aharonov Y. and Bohm D, Significance of electromagnetic potentials in the quantum theory, Physical Revie 115, 485, 1959
  3. Chamners R. G., Shift of an electron interference pattern by enclosed magnetic flux, Phys. Rev. Lett. 5, 3, 1960
  4. Majkic Z., Partial Differential Equations for Wave Packets in the Minkowski 4-dimensional Spaces, Differencialnie uravnenia i protsesy upravlenia, no. 1(2011), http://www.math.spbu.ru/diffjournal/pdf/madjkic.pdf , 2011
  5. Majkic Z., Completion and Unification of Quantum Mechanics with Einstein's GR Ideas, Part I: Completion of QM, Nova Science Publishers, New York, ISBN:978-1-53611-946-6, July, 2017
  6. Majkic Z., Completion and Unification of Quantum Mechanics with Einstein's GR Ideas, Part II: Unification with GR, Nova Science Publishers, New York, ISBN:978-1-53611-947-3, September, 2017
  7. Majkic Z., Completion and Unification of Quantum Mechanics with Einstein's GR Ideas, Part III: Advances, Revisions and Conclusions, Nova Science Publishers, New York, ISBN:978-1-53617-200-3, November, 2019
  8. Osakabe N., at all. Experimental confirmation of AharonovBohm effect using a toroidal magnetic field confined by a superconductor, Physical Review A. 34 (2), 1986
  9. Majkic Z., Double-slit Experiment: a Test for Individual Particles Completion of Quantum Mechanics, Differencialnie uravnenia i protsesy upravlenia, no. 2(2019), Publisher: Mathematics and Mechanics Faculty of Saint-Petersburg State University, Russia, http://www.math.spbu.ru/diffjournal/pdf/madjkic.pdf , 2019
  10. Majkic Z., Hydrodynamic equilibrium and stability for particle's energy-density wave-packets: \textsc{S}tate and revision, Differencialnie uravnenia i protsesy upravlenia, no. 3(2018), Publisher: Mathematics and Mechanics Faculty of Saint-Petersburg State University, Russia, http://www.math.spbu.ru/diffjournal/pdf/madjkic.pdf , 2018
  11. Majkic Z., Schrodinger Equation and Wave Packets for Elementary Particles in the Minkowski Spaces, Differencialnie uravnenia i protsesy upravlenia, no. 3(2011), Publisher: Mathematics and Mechanics Faculty of Saint-Petersburg State University, Russia, http://www.math.spbu.ru/diffjournal/pdf/madjkic2.pdf , 2011
  12. Majkic Z., Differential Equations for Elementary Particles: Beyond Duality, LAP LAMBERT Academic Publishing, Saarbrucken, Germany, 2013
  13. Jackson J. D., Classical Electrodynamics, (3rd ed. ). Wiley, 1998
  14. Adelberger E., Dvali G., Gruzinov A., Photon Mass Bound Destroyed by Vortices, Phys. Rev. Lett. 98:010402, 2007
  15. Gibs P., Is The Speed of Light Constant?, in Carlip, S. Usenet Physics FAQ. University of California, Riverside. http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed\_of\_light.html , 1997
  16. Sidharth B., The Thermodynamic Universe, World Scientific. p. 134. ISBN 9812812342, http://books.google.com/books?id=OUfHR36wSfAC\&pg=PA134] , 2008
  17. Majkic Z., Derivation of Electromagnetism from Quantum Theory of Photons: Tesla Scalar Waves, E-Journal Differential Equations and Control Processes, N. 3, 2020, Publisher: Mathematics and Mechanics Faculty of Saint-Petersburg State University, Russia, 2020
  18. Shelankov A. L., Magnetic force exerted by the Aharonov-Bohm line, Europhys. Lett. 43, 623, 1998
  19. Berry M. V. J., Aharonov-Bohm beam deflection: Shelankov's formula, exact solution, asymptotics and an optical analogue, J. Phys. A: Math. Gen. 32, 5627, 1999
  20. Becker M, and Guzzinati G. and Armand B. and Verbeeck J. and Batelaan H., Observation of Quantum Forces in the ., Aharonov-Bohm effect, arXiv: 1705. 07139, May, 2017
  21. Lifshitz E. M. and Pitaevskij L. P., Zh. \textsc{E}ksp. \textsc{T}eor. \textsc{F}iz. 33, 535 (1957), [Sov. Phys. -JETP 6, 418], 1958
  22. Iordanskij S. V., Zh. \textsc{E}ksp. \textsc{T}eor. \textsc{F}iz. 49, 225 (1965), [Sov. Phys. -JETP 22, 160], 1966
  23. Sonin E. B., Magnus force and ., Aharonov-Bohm effect in superfluids, arXiv:cond-mat 0104221, 2001
  24. Hehl F. W. and von der Heyde P. and Kerlick G. D. and J. M. Nester J. M., General relativity with spin and torsion: foundations and prospects, Rev. Mod. Phys. 48, N0. 3, 1976

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