A Uniform Static Magnetic Field in Kaluza-Klein Theory
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.
KeywordsManifold Sine Cote
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- 1.R.C. Accad. Lincei (5) 26, 519 (1917).Google Scholar
- 2.Bull. Akad. Pol. 7, 351 (1959).Google Scholar
- 3.Phys. Rev. 116, 1331 (1959).Google Scholar
- 4.W. Rindler and A. Trautman, editors. Robinson Festschrift, to be published. Bibliopolis, Napoli, Italy.Google Scholar
- 7.Gruppi Continui Finiti, Pg. 578, Pisa (1918).Google Scholar
- 8.Proc. Royal Soc. A133, 60 (1931).Google Scholar