= CP transformation of non-Abelian field strength
{c}
{title2=$\mathcal F_{\mu\nu}^{CP}=-P_\mu{}^\alpha P_\nu{}^\beta\mathcal F_{\alpha\beta}^T(x_P)$}
For $\mathcal F_{\mu\nu}=\partial_\mu\mathcal A_\nu-\partial_\nu\mathcal A_\mu+ig[\mathcal A_\mu,\mathcal A_\nu]$, the <CP transformation of a non-Abelian gauge connection> gives $\mathcal F_{\mu\nu}^{CP}(x)=-P_\mu{}^\alpha P_\nu{}^\beta\mathcal F_{\alpha\beta}^T(x_P)$. The commutator term transforms with the same sign as the derivative terms because $[X^T,Y^T]=-[X,Y]^T$. A simple component check is $F_{0i}\mapsto+F_{0i}^T$ and $F_{ij}\mapsto-F_{ij}^T$, evaluated at the reflected point.
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