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

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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).

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References

  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).

  2. Yu. S. Vladimirov, Classical Theory of Gravitation [in Russian], Librokom, Moscow (2009).

    Google Scholar 

  3. D. O. Dziakovych, “Geometrization of electromagnetism in a space with torsion” Zh. Fiz. Doslid.,18, No. 2-3, 2001-1–2001-5 (2014).

    MathSciNet  Google Scholar 

  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).

  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. Y. Lam, “Totally asymmetric torsion on Riemann–Cartan manifold”; http://arxiv.org/abs/gr-qc/0211009v12002.

  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.

    Chapter  Google Scholar 

  8. J. M. Overduin and P. S. Wesson, “Kaluza–Klein gravity,” Phys. Rept.,283, No. 5-6, 303–378 (1997).

    Article  MathSciNet  Google Scholar 

  9. P. S. Wesson, Space, Time, Matter: Modern Kaluza–Klein Theory, World Scientific, Singapore (1999).

  10. H.-J. Xie and T. Shirafuji, “Torsion field equation and spinor source,” Progr. Theor. Phys.,97, No. 1, 129–140 (1997).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Ukrainian Research Institute for Elastomeric Materials and Products, Dnipro, Ukraine

    D. О. Dziakovych

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  1. D. О. Dziakovych
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 60, No. 2, pp. 51–56, April–June, 2017.

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Dziakovych, D.О. Justification of the Kaluza–Klein Theory within the Framework of Four-Dimensional Riemann–Cartan Geometry. J Math Sci 243, 56–62 (2019). https://doi.org/10.1007/s10958-019-04525-1

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  • DOI: https://doi.org/10.1007/s10958-019-04525-1

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