= Ghost propagator for a negative derivative kinetic term
{title2=$\langle Tc^a(x)\bar c^b(y)\rangle=\delta^{ab}\int d^4p\,(2\pi)^{-4}e^{-ip(x-y)}[-i/(p^2+i0)]$}
With signature $(+---)$ and action $-\int\partial^\mu\bar c\,\partial_\mu c$, integration by parts gives the quadratic kernel $K_c=\Box$, or $-p^2$ in Fourier space. The <Grassmann Gaussian integral> with odd sources gives $Z=\exp[-i\bar\eta K_{c,F}^{-1}\eta]$. Left and right source derivatives, including their insertion factors, yield $\langle Tc\bar c\rangle=iK_{c,F}^{-1}$ and hence the displayed sign. Replacing $\bar c$ by $-\bar c$ changes this propagator and the <ghost-gluon vertex> together; it is a convention change, not a physical discrepancy.
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