Covariant gauge-fixing density as a BRST variation (source code)

= Covariant gauge-fixing density as a BRST variation
{title2=$\mathcal L_{\rm gf+gh}=s[-\bar c^a(\partial^\mu A_\mu^a+\xi b^a/2)]$}

For the left <graded Leibniz rule> and $s\bar c=-b$, $sb=0$, the displayed <gauge-fixing fermion> gives $b\,\partial\cdot A+\xi b^2/2+\bar c\,\partial\cdot Dc$. The ghost signs follow from odd parity. <BRST nilpotence> implies invariance of this density without using field equations. Eliminating the <Nakanishi-Lautrup field> gives $-(\partial\cdot A)^2/(2\xi)$ for nonzero $\xi$.