Polchinski equation
= Polchinski equation
{c}
{title2=$\dot S_1=\tfrac12\dot C:(S_1'S_1'-S_1'')$}
The <Polchinski equation> changes an interaction action with its regulated Gaussian covariance so that the normalized <functional integral> stays unchanged. In operator notation, $\dot e^{-S_1}=-\dot C:\delta^2e^{-S_1}/2$. The resulting action flow has a product of first <functional derivatives>, joining two vertices, and a second derivative, closing two legs into a loop. It generates a <Wilsonian effective action>, which is not the same functional as the <one-particle-irreducible correlation functions> encoded by the <quantum effective action>.