Bogomolny-Prasad-Sommerfield monopole

A Bogomolny-Prasad-Sommerfield monopole is a finite-energy Yang-Mills-Higgs configuration satisfying $B_i=\pm D_i\Phi$. Its magnetic charge is the degree of the normalized Higgs field at spatial infinity.

A spherically symmetric SU(2) monopole can be written with the internal Higgs direction aligned with the spatial radial direction and the gauge field built from the invariant tensor ${ϵ}_{aij}$.