= Charge conjugation of a non-Abelian gauge field
{title2=$\mathcal A_\mu\mapsto-\mathcal A_\mu^T$}
Write a matrix-valued <gauge field> $\mathcal A_\mu=A_\mu^aT^a$ in the <fundamental representation>. <Charge conjugation> sends it to $-\mathcal A_\mu^T$ because reordering the fermions transposes both the spinor and internal matrices. The identity $[A^T,B^T]=-[A,B]^T$ then sends the <gauge field strength> to $-\mathcal F_{\mu\nu}^T$. This distinction prevents treating all color components as individually C-odd.
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