Dual fiber bundles, the size of the fifth dimension and dirac magnetic monopoles

Abstract

We introduce a dual-fiber-bundle description of the gauge theory of electromagnetism. Using this, and requiring particles to obey the wave equation in the five-dimensional fiber bundle, we show that the existence of a given unique radius for the compact fifth dimension breaks the duality transformation invariance of the theory. One of the reasons for the possible existence of magnetic monopoles is the very pretty duality invariance of Maxwell’s equations achieved if magnetic currents are present. Since we show that this duality transformation invariance is broken if we try to extend it to the fiber bundle formulation, the existence of Dirac magnetic monopoles becomes somewhat less compelling theoretically.