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

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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 ħ → 0 and the speed of light c→ ∞.

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Authors and Affiliations

  1. Steklov Mathematical Institute, RAS, Moscow, Russia

    N. N. Bogolubov Jr.

  2. Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

    N. N. Bogolubov Jr.

  3. Department of Applied Mathematics, AGH University of Science and Technology, Krakow, Poland

    A. K. Prykarpatsky

  4. Ivan Franko State Pedagogical University, Drogobych, Lviv Oblast, Ukraine

    A. K. Prykarpatsky

  5. Department of Applied Mathematics and Computer Science, Eastern Mediterranean University, Famagusta, Cyprus

    U. Taneri

  6. Institute of Graduate Studies, Kyrenia American University, Kyrenia, Cyprus

    U. Taneri

Authors
  1. N. N. Bogolubov Jr.
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  2. A. K. Prykarpatsky
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  3. U. Taneri
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Correspondence to N. N. Bogolubov Jr..

Additional information

Dedicated to Academician Nikolai Nikolaevich Bogoliubov in honor of his 100th birthday in sincere recognition of his brilliant talent and impressive contribution to modern nonlinear mathematics and quantum physics

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 2, pp. 249–269, August, 2009.

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Bogolubov, N.N., Prykarpatsky, A.K. & Taneri, U. The vacuum structure, special relativity theory, and quantum mechanics: A return to the field theory approach without geometry. Theor Math Phys 160, 1079–1095 (2009). https://doi.org/10.1007/s11232-009-0101-8

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  • DOI: https://doi.org/10.1007/s11232-009-0101-8

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