Definition: Unpolarized and polarized source summands

For a smooth symmetric $\gamma$ put

so that ${\mathcal{J}}_{\mathrm{D}}={\mathfrak{s}}_{J_3}+{\mathfrak{s}}_{C_2}+{\mathfrak{s}}_{M_2}$ by (eq:L-JD). For $A\in \{C_2,M_2,J_3\}$ and smooth symmetric $X,Y$, the polarization is XII-D's rule, as used in XVI-K, Definition def:a:

$X$ and $Y$ are the two contracted field slots (the increments carried by the two edges in L.2). No residual metric $h$ enters ${\mathfrak{s}}_A$: the source is quadratic in the slot fields alone, and $h$ enters the graph only through the vertex ${L^{pq}}_{ij}(w;h)$.