Topological characterization of charge quantization
ABSTRACT Weinberg has written a paper showing how to calculate gauge coupling constants in (4 +N)dimensional models withN dimensions forming a compact manifold. Each coupling constant is related to the inverse of an appropriate rootmeansquare
circumference of the manifold. We extend this work by showing that this charge is quantized, in the sense of a tower of particles
each carrying a charge which is an integer multiple of a basic unit, if and only if Π1(I) =ZZ where Π1 is the first homotopy group,I is the isometry group of the compact manifold, andZZ is the additive group of integers.
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 01/1987; Academic Press.

Article: Fivedimensional relativity
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ABSTRACT: We study the hypothesis where the universe U is a fivedimensional Riemannian manifold, wich satisfies certain global topological conditions. We postulate the existence of a principle of relativity wich treats on equal basis the live dimensions of U; the laws wich satisfy this principle have an approximate description in a 4dimensional spacetime manifold û; this gives the possibility of comparing them with the usual description of experimental laws. Thus, if we extend to the fifth dimension the invariance of general relativity, we obtain classical electrodynamics: the equations of Maxwell, conservation of electricity, electromagnetic forces, etc. Likewise, the fivedimensional extension of the invariance of the wave equations leads one automatically to electromagnetic terms, such as they are actually observed; the electric charge, for instance, is found to be an integral multiple of an elementary charge which depends neither on the mass, nor on the spin. Among the other consequences of the theory, we find gauge invariance, and charge conjugation; the maximum violation of parity in Βdecays; the existence of two neutrinos of opposite chirality.Il Nuovo Cimento 09/1963; 30(2):565578. DOI:10.1007/BF02828833  [Show abstract] [Hide abstract]
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