Global gauge transformations and conserved, gauge-invariant electric and magnetic charges in Yang-Mills gauge theories.

Abstract

We construct gauge-invariant, conserved electric and magnetic charges in gauge theories of the Yang-Mills type. Global gauge transformations play a central role in defining these charges. As an illustration, we demonstrate explicitly how this definition of charges provides a finer classification than ${\ensuremath{\pi}}_{1}$(SO(3)) for the non-Abelian SO(3) monopoles of the Dirac type. In our formulation, the problem of global color in the presence of a magnetic monopole is transparent and it is in fact a general phenomenon in theories involving nontrivial principal fiber bundles with non-Abelian gauge groups.