# 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.

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.

## References

• M.V. Goganov and L.V. Kapitansii, "Global solvability of the initial problem for Yang-Mills-Higgs equations", Zapiski LOMI 147,18-48, (1985); J. Sov. Math, 37, 802-822 (1987).