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.
KeywordsMagnetic Monopole Homogeneous Magnetic Field Newtonian Gravitational Constant Advance Lead Uniform Static Magnetic Field
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