Spherically symmetric monopoles

Abstract

The task of finding all spherically symmetric three-dimensional point monopoles in a gauge theory with arbitrary compact semisimple group is completely formulated in an Abelian gauge, where the problem is purely group-theoretical. The form of the gauge transformation to the spherically symmetric gauge is explicitly given in the general case. For $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ groups this result is reduced to a simple diagrammatic method which yields all such point monopoles by inspection. Also for $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ groups, a technique is given for efficient construction of the radial differential equations satisfied by the corresponding finite-energy solutions.