By using the heat kernel method, we construct diffeomorphism-covariant coherent states for the $SU(3)$ gauge group. We numerically demonstrate that these states exhibit the required semiclassical properties in the semiclassical limit: the peakedness property of the probability distribution and the peakedness property of the overlap function. We also provide the leading-order term of the overlap amplitude in the combined limit where $t\to 0$ and $g\to g^{\prime }$. This work provides the essential tool for deriving effective dynamics for $SU(3)$ gauge fields coupled to gravity via a coherent state path integral.

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• Loop quantum gravity
• Quantum gravity