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

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

${\displaystyle D_{A}*D_{A}\Phi =0}$

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. They are very closely related to the Ginzburg–Landau equations, when these are expressed in a general geometric setting.

M.V. Goganov and L.V. Kapitanskii have shown that the Cauchy problem for hyperbolic Yang–Mills–Higgs equations in Hamiltonian gauge on 4-dimensional Minkowski space have a unique global solution with no restrictions at the spatial infinity. Furthermore, the solution has the finite propagation speed property.