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
with a boundary condition
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.
- 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).
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