Ghost and auxiliary cancellation

The half-normalized metric differential is $s_0\gamma =\mathcal{R}c$. The gauge fermion produces $i\bar{c}\square c$, not $2i\bar{c}\square c$.

Its causal anticommutator is

while $[\gamma ,b]=i\hslash \mathcal{R}{\delta }_0$. These exact coefficients produce the cancellation in Theorem thm:differential. Replacing one coefficient without rescaling the ghost would destroy that compatibility.

One could instead use the full ghost normalization $s_0\gamma =K\tilde{c}$, with $c=2\tilde{c}$. Then the corresponding ghost kinetic coefficient changes. That is an equivalent reparametrization, not a second gauge chosen in this paper.