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 (specifically, the adjoint bundle). These equations are D A ∗ F A + ∗ [ Φ , D A Φ ] = 0 , D A ∗ D A Φ = 0 {\displaystyle {\begin{aligned}D_{A}*F_{A}+*[\Phi ,D_{A}\Phi ]&=0,\\D_{A}*D_{A}\Phi &=0\end{aligned}}} with a boundary condition lim | x | → ∞ | Φ | ( x ) = 1 {\displaystyle \lim _{|x|\rightarrow \infty }|\Phi |(x)=1} where A is a connection on a vector bundle, DA is the exterior covariant derivative, FA is the curvature of that connection, Φ is a section of that vector bundle, ∗ is the Hodge star, and [·,·] is the natural, graded bracket.

Source: Wikipedia — Yang–Mills–Higgs equations (CC BY-SA 4.0)

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 (specifically, the adjoint bundle). These equations are D A ∗ F A + ∗ [ Φ , D A Φ ] = 0 , D A ∗ D A Φ = 0 {\displaystyle {\begin{aligned}D_{A}*F_{A}+*[\Phi ,D_{A}\Phi ]&=0,\\D_{A}*D_{A}\Phi &=0\end{aligned}}} with a boundary condition lim | x | → ∞ | Φ | ( x ) = 1 {\displaystyle \lim _{|x|\rightarrow \infty }|\Phi |(x)=1} where A is a connection on a vector bundle, DA is the exterior covariant derivative, FA is the curvature of that connection, Φ is a section of that vector bundle, ∗ is the Hodge star, and [·,·] is the natural, graded bracket.

Source: Wikipedia "Yang–Mills–Higgs equations" · CC BY-SA 4.0

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