View source for Yang–Mills–Higgs equations

In mathematics, the '''Yang–Mills–Higgs equations''' are a set of [[non-linear partial differential equation]]s for a [[Yang–Mills field]], given by a connection, and a [[Higgs field]], given by a section of a [[vector bundle]]. These equations are 
:<math>D_A*F_A+[\Phi,D_A\Phi]=0,</math>
:<math>D_A*D_A\Phi=0</math> 
with a [[boundary condition]] 
:<math>\lim_{|x|\rightarrow \infty}|\Phi|(x)=1.</math>

These equations are named after [[Chen Ning Yang]], [[Robert Mills (physicist)|Robert Mills]], and [[Peter Higgs]].  They are very closely related to the [[Ginzburg–Landau theory|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.

==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).

{{Quantum field theories}}

{{DEFAULTSORT:Yang-Mills-Higgs equations}}
[[Category:Partial differential equations]]


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