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 TMF, 2009, Volume 160, Number 2, Pages 249–269 (Mi tmf6396)

The vacuum structure, special relativity theory, and quantum mechanics: A return to the field theory approach without geometry

N. N. Bogolyubov (Jr.)ab, A. K. Prikarpatskiicd, U. Tanerief

a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
c Ivan Franko State Pedagogical University, Drogobych, Ukraine
d The AGH University of Science and Technology, Department of Applied Mathematics, Krakow, Poland
e Eastern Mediterranean University, Department of Applied Mathematics and Computer Science, Famagusta
f Kyrenia American University, Institute of Graduate Studies, Kyrenia, Cyprus

Abstract: We formulate the main fundamental principles characterizing the vacuum field structure and also analyze the model of the related vacuum medium and charged point particle dynamics using the developed field theory methods. We consider a new approach to Maxwell's theory of electrodynamics, newly deriving the basic equations of that theory from the suggested vacuum field structure principles; we obtain the classical special relativity theory relation between the energy and the corresponding point particle mass. We reconsider and analyze the expression for the Lorentz force in arbitrary noninertial reference frames. We also present some new interpretations of the relations between special relativity theory and quantum mechanics. We obtain the famous quantum mechanical Schrödinger-type equations for a relativistic point particle in external potential and magnetic fields in the semiclassical approximation as the Planck constant $\hbar\to0$ and the speed of light $c\to\infty$.

Keywords: vacuum structure, local mass conservation law, local momentum conservation law, Lorentz force, relativity theory

DOI: https://doi.org/10.4213/tmf6396

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English version:
Theoretical and Mathematical Physics, 2009, 160:2, 1079–1095

Bibliographic databases:

Citation: N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, U. Taneri, “The vacuum structure, special relativity theory, and quantum mechanics: A return to the field theory approach without geometry”, TMF, 160:2 (2009), 249–269; Theoret. and Math. Phys., 160:2 (2009), 1079–1095

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf6396
• https://doi.org/10.4213/tmf6396
• http://mi.mathnet.ru/eng/tmf/v160/i2/p249

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Bogolubov N.N. (Jr.), Prykarpatsky A.K., “The Lagrangian and Hamiltonian analysis of some relativistic electrodynamics models and their quantization”, Condensed Matter Physics, 12:4 (2009), 603–616
2. Bogolubov N.N., Jr., Prykarpatsky A.K., Taneri U., “The relativistic electrodynamics least action principles revisited: new charged point particle and hadronic string models analysis”, Internat. J. Theoret. Phys., 49:4 (2010), 798–820
3. Slawianowski J.J., “Geometric nonlinearities in field theory, condensed matter and analytical mechanics”, Condensed Matter Physics, 13:4 (2010), 43103
4. Prykarpatsky A.K., “Reminiscences of unforgettable times of my collaboration with Nikolai N. Bogolubov (Jr.) Foreword”, Condensed Matter Physics, 13:4 (2010), 40102
5. Bogolubov N.N. (Jr.), Prykarpatsky A.K., “The vacuum structure and special relativity revisited: A field theory no-geometry approach within the Lagrangian and Hamiltonian formalisms”, Physics of Particles and Nuclei, 41:6 (2010), 913–920
6. Bogolubov N.N. (Jr.), Prykarpatsky A.K., “The Analysis of Lagrangian and Hamiltonian Properties of the Classical Relativistic Electrodynamics Models and Their Quantization”, Found. Phys., 40:5 (2010), 469–493
7. Prykarpatsky A.K., Bogolubov Nikolai N. Jr., “The Maxwell Electromagnetic Equations and the Lorentz Type Force Derivation-The Feynman Approach Legacy”, Internat J Theoret Phys, 51:1 (2012), 237–245
8. Prykarpatsky A.K., Bogolubov Jr. N. N., “On the Classical Maxwell–Lorentz Electrodynamics, the Electron Inertia Problem, and the Feynman Proper Time Paradigm”, Ukr. J. Phys., 61:3 (2016), 187–212
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