Article

# 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.

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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