This article is cited in 11 papers

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. Prikarpatskii^cd, U. Taneri<sup>ef

a</sup> 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.

Received: 20.08.2008

DOI: 10.4213/tmf6396

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

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