Source action

Builder/output: source_action.py (unchanged since p10).

$S_{\mathrm{af}}={\sum }_A{\sigma }_A\int {\Phi }_A^{\ast }s{\Phi }^A$ (antifield on the left). Requiring the generator rule $(S,{\Phi }^A)=s{\Phi }^A$ with the XVI-N bracket derives ${\sigma }_A=(-1{)}^{|{\Phi }^A|}$: ${\sigma }_h={\sigma }_{\varphi }=+1$, ${\sigma }_c={\sigma }_{\bar{c}}=-1$. The nonminimal coupling $-\int {\bar{c}}^{\ast \mu }i{b}_{\mu }$ is included; $b^{\ast }$ does not occur ($sb=0$). $X=S_{\mathrm{af}}$ has ghost number $0$, is antifield-linear, and has 17 / 124 / 0 terms at ${\kappa }^0/{\kappa }^1/{\kappa }^2$. Because $X$ is linear in antifields, $(S,S)=2(S_{\mathrm{field}},X)+(X,X)$ with $2(S_{\mathrm{field}},X)=2\int E_{\Phi }(S_{\mathrm{field}})\sigma s\Phi$ of antifield number 0 and $(X,X)=-2\sum {\Phi }^{\ast }{s}^2\Phi$ (mod $d$) of antifield number 1.