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The color language is not really well-suited to understand why there are eight gluons. Here's why, however: The gluon field transforms in the adjoint representation of the color gauge group $\mathrm{SU}(3)$. The adjoint representation is a representation on the vector space of the generators of $\mathrm{SU}(3)$, the Lie algebra $\mathfrak{su}(3)$. An ...

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