 Ghost propagator

A ghost propagator is the two-point function $⟨Tc(x)\bar{c}(y)⟩$ of a Faddeev-Popov ghost field and its independent Faddeev-Popov antighost field. For quadratic action $\int \bar{c}Mc$ and source ordering consistent with that field ordering, the Grassmann integral gives $G_c=i{M}_F^{-1}$. The subscript specifies the causal pole prescription. For the negative derivative kinetic term $-\int \partial \bar{c}\cdot \partial c$, the Fourier kernel is $M=-p^2$. With signature $(-,+,+,+)$ this gives $G_c=-i/(p^2-i0)$. Field normalization multiplies the inverse kernel accordingly, while an antighost sign redefinition changes propagator and vertex signs together. Anticommuting statistics and loop signs do not turn these auxiliary fields into physical asymptotic particles.