All roads lead to the Dirac quantization condition

Abstract

The existence of magnetic monopoles is a sufficient argument to explain the quantization of electric charge, an argument that was presented by Dirac. Regardless of the status of any search for magnetic monopoles, the formal description of the quantum mechanics of a charged particle in the field of a magnetic monopole is very rich and has increased our understanding of the mathematical structures underlying this description, as well as of its physical implications. In this short review, we present four different arguments all leading to the Dirac quantization condition, emphasizing their geometrical and topological aspects.