= Yang-Mills theory coupled to an arbitrary scalar representation
{c}
{title2=$\mathcal L=-B(\mathcal F,\mathcal F)/(4g^2)+h(D\Phi,D\Phi)-V$}
For a compact simple <gauge group>, use $B=-\kappa$ on its algebra and an averaged positive invariant <Hermitian form> $h$ on any supplied finite-dimensional complex representation. With anti-Hermitian connection and signature $(+---)$, $\mathcal L=-B(\mathcal F_{\mu\nu},\mathcal F^{\mu\nu})/(4g^2)+h(D_\mu\Phi,D^\mu\Phi)-V(\Phi)$ is <gauge-invariant> whenever $V$ is invariant. A real scalar representation instead has a symmetric form and kinetic prefactor $1/2$.
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