= Derrick scaling of Yang-Mills-Higgs energy
{c}
{title2=$V_\lambda=\lambda V_B+\lambda^{-1}V_D+\lambda^{-3}V_U$}
In three space dimensions, rescale $A_i(x)$ to $\lambda A_i(\lambda x)$ and $\Phi(x)$ to $\Phi(\lambda x)$. The <gauge curvature> then scales with two derivatives, and the <adjoint covariant derivative> of the <Higgs field> with one. Magnetic, Higgs-gradient and potential energies give the displayed formula. Stationarity requires $V_B=V_D+3V_U$, which permits nonzero energies. In the <Bogomolny-Prasad-Sommerfield monopole> limit $V_U=0$, the <Bogomolny equations> give $V_B=V_D$.
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