Covariantly constant vector Higgs field
= Covariantly constant vector Higgs field
{title2=$D_\mu\Phi=0$}
If $D_\mu\Phi=0$ in the <SO(3) vector Higgs model>, antisymmetry of the <gauge potential> implies $\partial_\mu|\Phi|^2=0$. On a local patch with nonzero constant norm, <unitary gauge> aligns the field with a fixed axis. The connection and <gauge field strength> then take values in the axis stabilizer; curvature can remain nonzero. Global alignment can require several bundle patches.