= Euclidean adjoint Dirac Feynman rules
{c}
Take Hermitian generators with $[T^a,T^b]=if^{abc}T^c$, $(T^b_{\mathrm{ad}})_{ac}=-if^{bac}$, and $D_\mu=\partial_\mu-igA_\mu^bT^b_{\mathrm{ad}}$. For $S_\psi=\int\bar\psi(\gamma_\mu D_\mu+m)\psi$ and $\{\gamma_\mu,\gamma_\nu\}=2\delta_{\mu\nu}$, the <Dirac propagator> is $\delta^{ac}(-i\not p+m)/(p^2+m^2)$. Expansion of $e^{-S_\psi}$ gives the fermion-gluon vertex $+ig\gamma_\mu(T^b_{\mathrm{ad}})_{ac}$. There is no two-gluon seagull vertex in this first-order kinetic action, and a closed fermion loop has a minus sign.
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