# Yang–Mills–Higgs equations

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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

${\displaystyle D_{A}*F_{A}+[\Phi ,D_{A}\Phi ]=0,}$
${\displaystyle D_{A}*D_{A}\Phi =0}$

with a boundary condition

${\displaystyle \lim _{|x|\rightarrow \infty }|\Phi |(x)=1.}$

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