New Approach to Geometrization of Electromagnetic Field

O. A. Olkhov

doi:doi:10.11648/j.ajpa.20150306.16

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New Approach to Geometrization of Electromagnetic Field

O. A. Olkhov

Published in American Journal of Physics and Applications (Volume 3, Issue 6)

Received: 2 December 2015 Accepted: 14 December 2015 Published: 30 December 2015

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Abstract

The new approach to geometrization of electromagnetic field is suggested, where previous author’s results on geometrical interpretation of quantum objects are taken into account. These results can be considered as a justification for considering of spaces with higher dimensions for geometrization of electromagnetic field. Electromagnetic fields and potentials are considered here as components of torsion tensor in 5-dimensional affinely connected space where the usual 4-space-time is a pseudo-Euclidean hyperplane. Electromagnetic potentials and tensor of electromagnetic field are represented by different components of the torsion tensor as it should be for the notions of different physical meaning. Suggested geometrization is free of such disadvantages of the known 5-dimensional Kaluza’s theory as the absence of physical foundations for introduction of additional spatial dimensions and the lack of any relationship with quantum mechanics.

Published in	American Journal of Physics and Applications (Volume 3, Issue 6)
DOI	10.11648/j.ajpa.20150306.16
Page(s)	221-225
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Geometrical Paradigm, Geometrical Interpretation of Quantum Mechanics, Geometrization of Electromagnetic Field

References

[1]	Th. Kaluza, “On the Unification Problem in Physics,” Sitzungsberichte Pruss. Acad. Sci, pp. 966-972, 1921.
[2]	A. Einstein and P. Bergmann, “On A Generalization of Kaluza’s Theory of Electricity”, Annals of Mathematics 39 p. 685, 1938.
[3]	Y. S. Vladimirov, Geometrophysics (in Russian). Moscow, Binom, 2005.
[4]	O. A. Olkhov. “Geometrization of Quantum Mechanics,” Journal of Phys.: Conf. Ser. vol. 67, p. 012037. 2007.
[5]	O. A. Olkhov. “Geometrization of Classical Wave fields,” Mellwill, New York, AIP Conference Proceedings p. 316, vol. 962, 2008 (Proc. Int. Conf. “Quantum Theory: Reconsideration of Foundations.” Vaxje, Sweden. 11-16 June, 2007).
[6]	O. A. Olkhov, “Geometrization of matter wave fields and electromagnetic waves,” Proc. of X111 Int. Scientific Meeting PIRT—2007, p. 318, Moscow; 2-5 July, 2007. Moscow-Liverpool-Sanderland.
[7]	O. A. Olkhov, “On the possibility of topological interpretation of quantum mecanics”, arXiv: 0802. 2269, 2008.
[8]	O. A. Olkhov. “Geometrical approach to the atomic spectra theory. The helium atom,” Russian J. of Phys. Chemistry B, vol. 8, pp. 30---42, February 2014 [Chim, Fis, p. 36, vol. 33, №2, 2014].
[9]	Oleg Olkhov. “Geometrical approach in atomic physics: Atoms of hydrogen and helium,” American Journal of Physics and Applications, vol. 2, №5, pp. 108---113, 2014.
[10]	Y. Aharonov and D. Bohm, “Significance of electromagnetic potentials in quantum theory,” Phys. Rev, vol. 115, pp. 485---491, 1959.
[11]	L. D. Landau, E. M. Lifshitz, Course of Theoretical Physics. Vol. 4; V. B. Berestetzki, E. M. Lifshitz, L. P. Pitaevski, Quantum Electrodynamics, Butterworth-Heinemann, 1982.
[12]	B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern geometry---Methods and Applications, Part 2: The Geometry and Topology of Manifolds, Springer, 1985.
[13]	A. S. Schwartz, Quantum field theory and topology, Grundlehren der Math. Wissen. 307, Springer, 1993.
[14]	H. S. M. Coxeter, Introduction to geometry, John Wiley & Sons, New York, London, 1961.
[15]	P. K. Rachevski. Riemannian geometry and tensor analisis (in Russian), Moscow, Nauka, 1966.
[16]	V. A. Jelnorovitch Theory of spinors and its applications (in Russian), Moscow, August-Print, 2001.
[17]	Ta-Pei Cheng, Ling-Fong Li, Gauge theory of elementary particle physics, Oxford, Clarendon Press, 1984.
[18]	Sharon Eitan. “Towards a geometrical foundation for physics,” SOP Transaction on Theoretical Physics, vol. 2, №1, pp. 89---129, 2015.

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O. A. Olkhov. (2015). New Approach to Geometrization of Electromagnetic Field. American Journal of Physics and Applications, 3(6), 221-225. https://doi.org/10.11648/j.ajpa.20150306.16

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O. A. Olkhov. New Approach to Geometrization of Electromagnetic Field. Am. J. Phys. Appl. 2015, 3(6), 221-225. doi: 10.11648/j.ajpa.20150306.16

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AMA Style

O. A. Olkhov. New Approach to Geometrization of Electromagnetic Field. Am J Phys Appl. 2015;3(6):221-225. doi: 10.11648/j.ajpa.20150306.16

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@article{10.11648/j.ajpa.20150306.16,
  author = {O. A. Olkhov},
  title = {New Approach to Geometrization of Electromagnetic Field},
  journal = {American Journal of Physics and Applications},
  volume = {3},
  number = {6},
  pages = {221-225},
  doi = {10.11648/j.ajpa.20150306.16},
  url = {https://doi.org/10.11648/j.ajpa.20150306.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20150306.16},
  abstract = {The new approach to geometrization of electromagnetic field is suggested, where previous author’s results on geometrical interpretation of quantum objects are taken into account. These results can be considered as a justification for considering of spaces with higher dimensions for geometrization of electromagnetic field. Electromagnetic fields and potentials are considered here as components of torsion tensor in 5-dimensional affinely connected space where the usual 4-space-time is a pseudo-Euclidean hyperplane. Electromagnetic potentials and tensor of electromagnetic field are represented by different components of the torsion tensor as it should be for the notions of different physical meaning. Suggested geometrization is free of such disadvantages of the known 5-dimensional Kaluza’s theory as the absence of physical foundations for introduction of additional spatial dimensions and the lack of any relationship with quantum mechanics.},
 year = {2015}
}

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TY  - JOUR
T1  - New Approach to Geometrization of Electromagnetic Field
AU  - O. A. Olkhov
Y1  - 2015/12/30
PY  - 2015
N1  - https://doi.org/10.11648/j.ajpa.20150306.16
DO  - 10.11648/j.ajpa.20150306.16
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 221
EP  - 225
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20150306.16
AB  - The new approach to geometrization of electromagnetic field is suggested, where previous author’s results on geometrical interpretation of quantum objects are taken into account. These results can be considered as a justification for considering of spaces with higher dimensions for geometrization of electromagnetic field. Electromagnetic fields and potentials are considered here as components of torsion tensor in 5-dimensional affinely connected space where the usual 4-space-time is a pseudo-Euclidean hyperplane. Electromagnetic potentials and tensor of electromagnetic field are represented by different components of the torsion tensor as it should be for the notions of different physical meaning. Suggested geometrization is free of such disadvantages of the known 5-dimensional Kaluza’s theory as the absence of physical foundations for introduction of additional spatial dimensions and the lack of any relationship with quantum mechanics.
VL  - 3
IS  - 6
ER  -

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Author Information

O. A. Olkhov

Department of Theoretical Physics, Institute of Chemical Physics, Moscow, Russia

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APA Style

O. A. Olkhov. (2015). New Approach to Geometrization of Electromagnetic Field. American Journal of Physics and Applications, 3(6), 221-225. https://doi.org/10.11648/j.ajpa.20150306.16

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ACS Style

O. A. Olkhov. New Approach to Geometrization of Electromagnetic Field. Am. J. Phys. Appl. 2015, 3(6), 221-225. doi: 10.11648/j.ajpa.20150306.16

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AMA Style

O. A. Olkhov. New Approach to Geometrization of Electromagnetic Field. Am J Phys Appl. 2015;3(6):221-225. doi: 10.11648/j.ajpa.20150306.16

Copy | Download

@article{10.11648/j.ajpa.20150306.16,
  author = {O. A. Olkhov},
  title = {New Approach to Geometrization of Electromagnetic Field},
  journal = {American Journal of Physics and Applications},
  volume = {3},
  number = {6},
  pages = {221-225},
  doi = {10.11648/j.ajpa.20150306.16},
  url = {https://doi.org/10.11648/j.ajpa.20150306.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20150306.16},
  abstract = {The new approach to geometrization of electromagnetic field is suggested, where previous author’s results on geometrical interpretation of quantum objects are taken into account. These results can be considered as a justification for considering of spaces with higher dimensions for geometrization of electromagnetic field. Electromagnetic fields and potentials are considered here as components of torsion tensor in 5-dimensional affinely connected space where the usual 4-space-time is a pseudo-Euclidean hyperplane. Electromagnetic potentials and tensor of electromagnetic field are represented by different components of the torsion tensor as it should be for the notions of different physical meaning. Suggested geometrization is free of such disadvantages of the known 5-dimensional Kaluza’s theory as the absence of physical foundations for introduction of additional spatial dimensions and the lack of any relationship with quantum mechanics.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - New Approach to Geometrization of Electromagnetic Field
AU  - O. A. Olkhov
Y1  - 2015/12/30
PY  - 2015
N1  - https://doi.org/10.11648/j.ajpa.20150306.16
DO  - 10.11648/j.ajpa.20150306.16
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 221
EP  - 225
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20150306.16
AB  - The new approach to geometrization of electromagnetic field is suggested, where previous author’s results on geometrical interpretation of quantum objects are taken into account. These results can be considered as a justification for considering of spaces with higher dimensions for geometrization of electromagnetic field. Electromagnetic fields and potentials are considered here as components of torsion tensor in 5-dimensional affinely connected space where the usual 4-space-time is a pseudo-Euclidean hyperplane. Electromagnetic potentials and tensor of electromagnetic field are represented by different components of the torsion tensor as it should be for the notions of different physical meaning. Suggested geometrization is free of such disadvantages of the known 5-dimensional Kaluza’s theory as the absence of physical foundations for introduction of additional spatial dimensions and the lack of any relationship with quantum mechanics.
VL  - 3
IS  - 6
ER  -

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