A Uniform Static Magnetic Field in Kaluza-Klein Theory

  • E. L. Schucking
Chapter
Part of the NATO ASI Series book series (NATO ASI)

Abstract

I shall report about work done with A. Rabinowitz. We studied a homogeneous magnetic field in the Kaluza-Klein theory. The complete five-dimensional manifold is not a direct product of the space-time manifold with a line or circle but has the topological structure of a three-dimensional sphere multiplied with a two-plane. Thus, compactification of the fifth dimension becomes a consequence of completeness. Moreover, the additional symmetries of the five-dimensional metric which are a consequence of the field equations and have not been postulated in advance lead already locally to a quantization of charge without postulating the existence of a magnetic monopole or an ad hoc compactification introduced by Oscar Klein.

Keywords

Manifold Sine Cote 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R.C. Accad. Lincei (5) 26, 519 (1917).Google Scholar
  2. 2.
    Bull. Akad. Pol. 7, 351 (1959).Google Scholar
  3. 3.
    Phys. Rev. 116, 1331 (1959).Google Scholar
  4. 4.
    W. Rindler and A. Trautman, editors. Robinson Festschrift, to be published. Bibliopolis, Napoli, Italy.Google Scholar
  5. 5.
    A. Lichnerowicz, Théories Relativistes de la Gravitation et de l’Electromagnetisme, Masson, Paris (1955).MATHGoogle Scholar
  6. 6.
    A. Trautman, Int. J. Theoretical Physics 16, 561 (1977).ADSCrossRefGoogle Scholar
  7. 7.
    Gruppi Continui Finiti, Pg. 578, Pisa (1918).Google Scholar
  8. 8.
    Proc. Royal Soc. A133, 60 (1931).Google Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • E. L. Schucking
    • 1
  1. 1.Physics DepartmentNew York UniversityNew YorkUSA

Personalised recommendations