Dirac monopoles and the Hopf map S³to S²

Abstract

It is shown that the presence of point magnetic monopoles necessitates a fibre-bundle formulation of electrodynamics. The Hopf 'fibring' of S3 over a base space S2 with fibre S1 yields the Wu-Yang potentials which describe the Dirac monopole. The Gauss-Bonnet-Chern theorem yields the Schwinger quantisation condition.