On the characterization of monopoles in non-Abelian gauge theories

Abstract

We attempt to help clarify some confusion in the literature on what characterizes monopoles in non-Abelian gauge theories. There is no meaningful classification of monopoles as “magnetic charge multiplets” belonging to representations of a “magnetic gauge geoup” as suggested by some authors, the “magnetic charge” defined there not being in general conserved We found no physically meaningful classification other than the topological quantum number or gauge type of bundles over spheres. For a pure su( n) Yang-Mills theory, this can be characterized by the nth roots of unity.