Connected shell-contraction expansion
= Connected shell-contraction expansion
{title2=$-\log\langle e^{-V}\rangle_>=\langle V\rangle_>-\tfrac12\langle V^2\rangle_{>,c}+\cdots$}
The <cumulant expansion> of the shell integral keeps precisely <connected Feynman diagrams> built from <shell-restricted scalar propagators>. The external low fields are backgrounds, not propagators. Connected graphs with bridges can contribute, so the expansion is not limited to <one-particle-irreducible Feynman diagrams>.