Gauge-fixing map in transformed variables

Builder/output: gauge_fixing_map.py.

$\Psi =-i\int {\bar{c}}_{\mu }(2D^{\mu }[h]-b^{\mu })$. The orientation $\epsilon =-1$ of ${\Phi }_A^{\ast }={{\Phi }^{\ast \prime }}_A+\epsilon \delta \Psi /\delta {\Phi }^A$ is derived from the Hessians, and $S_{\Psi }(\Phi ,{\Phi }^{\ast \prime }):=S(\Phi ,{\Phi }^{\ast \prime }-\delta \Psi /\delta \Phi )\simeq S+s\Psi$. Hessians at generic momentum (since p11). The $(h,b)$ Hessian $M$ is computed for a symbolic $k=(k_0,k_1,k_2,k_3)$. With $M=\left(\begin{array}{cc}A& B\\ C& D\end{array}\right)$, $\det D=-16\ne 0$, and the Schur complement satisfies $A-B{D}^{-1}C=k^{2}P$ identically in $\mathbb{Q}(k)$, with $\det (k^{2}P)=64(k^2{)}^{10}\ne 0$. The block-inverse formula then gives $(M^{-1}{)}_{hh}=(k^{2}P{)}^{-1}$ (graviton kernel $K=-\square P$). The ghost kinetic term $i\bar{c}\square c$ and the scalar $-\square$ are exact as well. No momentum sample is used. Canonicity is checked on all 23 antifield components (276 antifield/antifield pairs and 23 antifield/field pairs). Interface: ${\Gamma }_{\Psi }(\Phi ,{\Phi }^{\ast \prime }):=\Gamma (\Phi ,{\Phi }^{\ast \prime }-\delta \Psi /\delta \Phi )$ is a defined classical pullback/interface along the canonical antifield shift. It is not an independently established quantum gauge-change theorem; no quantum $\Gamma$ is constructed here.