= Centered four-point cumulant decomposition
{title2=$G_4=C_4+\sum C_2C_2$}
For a normalized Minkowski source functional $Z=e^{iW}$ with vanishing <one-point function>, $C_n=i^{1-n}\delta^nW/\delta J^n$ and
$$
G_{1234}=C_{1234}+C_{12}C_{34}+C_{13}C_{24}+C_{14}C_{23}.
$$
Differentiating $e^{iW}$ assigns the four labels to connected blocks. Blocks of size one vanish, leaving one block of four or one of the three pair partitions. Thus $G_4=iW_4-\sum W_2W_2$ in this source convention.
// Target: perturbative-quantum-field-theory.bigb
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