Conventions

Declared once in conventions.py.

$\eta =\mathrm{diag}(+,-,-,-)$; $g_{\mu \nu }={\eta }_{\mu \nu }+\kappa h_{\mu \nu }$ (affine in $h$); $S_{\mathrm{EH}}=-(2/{\kappa }^2)\int \sqrt{-g}R={\sum }_k{\kappa }^{k-2}\int {\ell }_k$ with ${\ell }_k=-2[{\epsilon }^k]L_{\Gamma \Gamma }$, $L_{\Gamma \Gamma }=\sqrt{-g}{g}^{\mu \nu }({{\Gamma }^{\lambda }}_{\mu \sigma }{{\Gamma }^{\sigma }}_{\nu \lambda }-{{\Gamma }^{\lambda }}_{\mu \nu }{{\Gamma }^{\sigma }}_{\lambda \sigma })$; $R^{\rho }{}_{\sigma \mu \nu }={\partial }_{\mu }{{\Gamma }^{\rho }}_{\nu \sigma }-{\partial }_{\nu }{{\Gamma }^{\rho }}_{\mu \sigma }+\Gamma \Gamma -\Gamma \Gamma$, $R_{\sigma \nu }=R^{\rho }{}_{\sigma \rho \nu }$. Massless scalar $S_{\varphi }=\frac{1}{2}\int \sqrt{-g}{g}^{\mu \nu }{\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$ with $\sqrt{-g}{g}^{\mu \nu }=\eta +\kappa a_1+{\kappa }^2{a}_2$ (XI-A, re-derived in P13_source_action). Ghost scaling ${\xi }^{\mu }=\kappa a{c}^{\mu }$, $a=\frac{1}{2}$. Antibracket (XVI-N def:antibracket)

Canonical pair for the graviton: $(h_{mn},K^{mn})$, $m\le n$. Divergence test (exact): a local density without constant term is a total divergence iff all its Euler derivatives vanish (contractible jet space).