= Vacuum functional
{title2=$Z[0]$}
The zero-<source> <generating functional> is the <vacuum state> persistence amplitude, conventionally written $Z[0]=\int\mathcal D\phi\,e^{iS[\phi]}$ with a suitable <Feynman i-epsilon prescription>. Dividing by $Z[0]$ removes disconnected <Vacuum Feynman diagrams> from normalized <Green functions>. Adding a constant <vacuum energy density> to the <Lagrangian density> changes $Z[0]$ by a spacetime-volume phase but leaves these normalized <Green functions> unchanged.
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