= Normalized vacuum generating functional
{title2=$\widehat Z[J]=Z[J]/Z[0]$}
For a vacuum <generating functional> $Z[J]$, normalization gives $\widehat Z[J]=Z[J]/Z[0]$ and $\widehat Z[0]=1$. <Functional derivatives> of $\widehat Z$ give normalized <vacuum expectation values>. The <linked-cluster theorem> shows that this ratio cancels <Vacuum Feynman diagrams>, while $-i\log\widehat Z[J]$ gives connected correlators. Components attached to external insertions are not removed merely by the normalization.
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