= 't Hooft-Polyakov monopole
{c}
A smooth finite-energy monopole in an $SU(2)$ <Yang-Mills theory> with an adjoint <Higgs field> uses the normalized Higgs direction at infinity to define a map $S^2_\infty\to S^2$. Its nonzero degree supplies the magnetic topological sector. Unlike a singular Abelian Dirac monopole, the non-Abelian gauge and Higgs fields can have a regular core. In the zero-potential limit the <Bogomolny-Prasad-Sommerfield monopole> equations are $B_i=\pm D_i\Phi$.
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