 Euclidean adjoint Dirac Feynman rules

Take Hermitian generators with $[T^a,T^b]=i{f}^{abc}{T}^c$, $(T_{\mathrm{ad}}^b{)}_{ac}=-i{f}^{bac}$, and $D_{\mu }={\partial }_{\mu }-ig{A}_{\mu }^b{T}_{\mathrm{ad}}^b$. 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 ${\delta }^{ac}(-i/p+m)/(p^2+m^2)$. Expansion of $e^{-S_{\psi }}$ gives the fermion-gluon vertex $+ig{\gamma }_{\mu }(T_{\mathrm{ad}}^b{)}_{ac}$. There is no two-gluon seagull vertex in this first-order kinetic action, and a closed fermion loop has a minus sign.