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
- Aharonov-Bohm effect
- Covariant derivative
- Interaction Processes
- Local symmetries
- Mathematical gauge theory
Ссылки:
- 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
- Aharonov Y. and Bohm D, Significance of electromagnetic potentials in the quantum theory, Physical Revie 115, 485, 1959
- Chamners R. G., Shift of an electron interference pattern by enclosed magnetic flux, Phys. Rev. Lett. 5, 3, 1960
- 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
- 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
- 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
- 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
- Osakabe N., at all. Experimental confirmation of AharonovBohm effect using a toroidal magnetic field confined by a superconductor, Physical Review A. 34 (2), 1986
- 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
- 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
- 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
- Majkic Z., Differential Equations for Elementary Particles: Beyond Duality, LAP LAMBERT Academic Publishing, Saarbrucken, Germany, 2013
- Jackson J. D., Classical Electrodynamics, (3rd ed. ). Wiley, 1998
- Adelberger E., Dvali G., Gruzinov A., Photon Mass Bound Destroyed by Vortices, Phys. Rev. Lett. 98:010402, 2007
- 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
- Sidharth B., The Thermodynamic Universe, World Scientific. p. 134. ISBN 9812812342, http://books.google.com/books?id=OUfHR36wSfAC\&pg=PA134] , 2008
- 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
- Shelankov A. L., Magnetic force exerted by the Aharonov-Bohm line, Europhys. Lett. 43, 623, 1998
- 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
- 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
- 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
- Iordanskij S. V., Zh. \textsc{E}ksp. \textsc{T}eor. \textsc{F}iz. 49, 225 (1965), [Sov. Phys. -JETP 22, 160], 1966
- Sonin E. B., Magnus force and ., Aharonov-Bohm effect in superfluids, arXiv:cond-mat 0104221, 2001
- 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