Advertisement

Journal of Mathematical Sciences

, Volume 243, Issue 1, pp 56–62 | Cite as

Justification of the Kaluza–Klein Theory within the Framework of Four-Dimensional Riemann–Cartan Geometry

  • D. О. Dziakovych
Article
  • 1 Downloads

We consider a new approach to the geometrization of electromagnetism based on the specific interpretation of the Kaluza–Klein theory. It is proposed to represent the five-dimensional space of this theory as a formal tool for the analysis of a four-dimensional space with torsion. For this purpose, we study the consequences of parametrization of a specific space of this type along the lines of the corresponding vector field that characterizes its geometry. It is shown that, within the framework of the new approach, all results of the Kaluza–Klein theory can be also obtained for a four-dimensional space with torsion (with some distinctions and generalizations).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. N. Aleksandrov, I. B. Vavilova, V. I. Zhdanov, A. I. Zhuk, Yu. N. Kudrya, S.L. Parnovsky, E. V. Fedorova, and Ya. S. Yatskiv, General Theory of Relativity: Recognition Through Time [in Russian], Naukova Dumka, Kiev (2015).Google Scholar
  2. 2.
    Yu. S. Vladimirov, Classical Theory of Gravitation [in Russian], Librokom, Moscow (2009).Google Scholar
  3. 3.
    D. O. Dziakovych, “Geometrization of electromagnetism in a space with torsion” Zh. Fiz. Doslid.,18, No. 2-3, 2001-1–2001-5 (2014).MathSciNetGoogle Scholar
  4. 4.
    L. D. Landau and E. M. Lifshits, Theoretical Physics, Vol. 2: Field Theory [in Russian], Nauka, Moscow (1988); English translation:A Course of Theoretical Physics, Vol. 2: Field Theory, Pergamon Press, Oxford (1987).Google Scholar
  5. 5.
    V. N. Ponomarev, A. O. Barvinskii, and Yu. N. Obukhov, Geometrodynamic Methods and the Calibration Approach to the Theory of Gravitational Interactions [in Russian], Énergoatomizdat, Moscow (1985).Google Scholar
  6. 6.
    Y. Lam, “Totally asymmetric torsion on Riemann–Cartan manifold”; http://arxiv.org/abs/gr-qc/0211009v12002.
  7. 7.
    I. Muntean, “Mechanisms of unification in Kaluza–Klein theory,” in: D. Dieks (editor), The Ontology of Spacetime II, Elsevier, Amsterdam (2008), pp. 275–300.CrossRefGoogle Scholar
  8. 8.
    J. M. Overduin and P. S. Wesson, “Kaluza–Klein gravity,” Phys. Rept.,283, No. 5-6, 303–378 (1997).MathSciNetCrossRefGoogle Scholar
  9. 9.
    P. S. Wesson, Space, Time, Matter: Modern Kaluza–Klein Theory, World Scientific, Singapore (1999).Google Scholar
  10. 10.
    H.-J. Xie and T. Shirafuji, “Torsion field equation and spinor source,” Progr. Theor. Phys.,97, No. 1, 129–140 (1997).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • D. О. Dziakovych
    • 1
  1. 1.Ukrainian Research Institute for Elastomeric Materials and ProductsDniproUkraine

Personalised recommendations