Yang–Mills–Higgs equations

In mathematics, the Yang–Mills–Higgs equations are a set of non-linear partial differential equations for a Yang–Mills field, given by a connection, and a Higgs field, given by a section of a vector bundle. These equations are

$D_A*F_A+[\Phi,D_A\Phi]=0,$

$D_A*D_A\Phi=0$

with a boundary condition

$\lim_{|x|\rightarrow \infty}|\Phi|(x)=1.$

These equations are named after Chen Ning Yang, Robert Mills, and Peter Higgs.