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There's one serious flaw in your entire strategy. Since $\overline{c},\,c$ are fermions, they are Grassmann-number-valued. Thus any complex numbers $w,\,z$ satisfy $(w\overline{c}+zc)^2=0$. You theref …

Let's consider perturbative quantum gravity as an example, with full metric $g_{\mu\nu}^f=g_{\mu\nu}+\kappa h_{\mu\nu}$. The Nakanishi-Lautrup auxiliary field and Faddeev-Popov ghost and antighost are …

Like any continuous symmetry, it represents a conservation law. The symmetry is manifest in the Lagrangian density term $-i\partial_\mu\bar{c}D^\mu c$, where $\bar{c}$ is cyclic. But if we add a total …

It's for the same reason they're unnecessary in Abelian theories. The FP-ghost term multiplies $e^{iS}$ by $\exp-\int d^4 x \bar{c}\partial_\mu D^\mu c=\det \partial_\mu D^\mu$, a determinant that can …

Faddeev-Popov ghosts can't be observed as particles because they violate the spin-statistics tension; Pauli-Villars ghosts are negative-norm states; the Landau pole tells you your theory must give way … to another at high energies; Goldstone ghosts represent an unphysical artefact of gauge fixing. …

As discussed in Kugo and Ojima 1979, "ghost is Hermitian, anti-ghost is anti-Hermitian" is just a convention, another being that both fields are Hermitian, which results in a factor of $i$ in the FP-g …