Ghost decoupling in strict axial gauge ($M=n\cdot D⟶n\cdot \partial$)

The Faddeev-Popov operator for $n\cdot A=0$ is $n\cdot D$. Its interaction contains $\bar{c}(n\cdot A)c$ and vanishes on the strict gauge slice. Equivalently, its ghost-gluon vertex is proportional to $n_{\mu }$ and the axial-gauge propagator obeys $n_{\mu }{D}^{\mu \nu }=0$. The residual determinant is field independent; its zero modes and $n\cdot p$ singularities still require a compatible axial-gauge pole prescription. Faddeev-Popov ghost decoupling does not mean that the free Faddeev-Popov ghost two-point function is zero.