Topological characterization of charge quantization

Il Nuovo Cimento A 06/1999; 112(6):639-645. DOI: 10.1007/BF03035874

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 rootmean-square
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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