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).
Similar content being viewed by others
References
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).
Yu. S. Vladimirov, Classical Theory of Gravitation [in Russian], Librokom, Moscow (2009).
D. O. Dziakovych, “Geometrization of electromagnetism in a space with torsion” Zh. Fiz. Doslid.,18, No. 2-3, 2001-1–2001-5 (2014).
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).
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).
Y. Lam, “Totally asymmetric torsion on Riemann–Cartan manifold”; http://arxiv.org/abs/gr-qc/0211009v12002.
I. Muntean, “Mechanisms of unification in Kaluza–Klein theory,” in: D. Dieks (editor), The Ontology of Spacetime II, Elsevier, Amsterdam (2008), pp. 275–300.
J. M. Overduin and P. S. Wesson, “Kaluza–Klein gravity,” Phys. Rept.,283, No. 5-6, 303–378 (1997).
P. S. Wesson, Space, Time, Matter: Modern Kaluza–Klein Theory, World Scientific, Singapore (1999).
H.-J. Xie and T. Shirafuji, “Torsion field equation and spinor source,” Progr. Theor. Phys.,97, No. 1, 129–140 (1997).
Author information
Authors and Affiliations
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 60, No. 2, pp. 51–56, April–June, 2017.
Rights and permissions
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-019-04525-1