Theory of Dirac monopoles with a non-Abelian symmetry

From the viewpoint of a global formulation of Yang-Mills fields, a Lagrangian theory of non-Abelian classical Dirac monopoles is proposed. Dirac strings are used instead of coordinate patches; they are defined as purely geometric constructs. The formalism is free from pathologies such as "Dirac's veto." While the analysis focuses on the gauge group $\mathrm{SU}\frac{\mathrm{}\left(N\right)\mathrm{}}{Z_N}$ allowing for only $N-1\mathrm{}$ nontrivial and topologically distinct types of monopoles, it applies in general to any compact Lie group.