Logarithmic-source inverse-kernel vertices (source code)

= Logarithmic-source inverse-kernel vertices
{title2=$\Gamma_2=-G_2^{-1},\quad\Gamma_3=(G_2^{-1})^{\otimes3}G_3^c$}

Use the Minkowski <generating functional> convention $Z=e^W$, source insertion $iJ\phi$, classical field $\varphi=-i\delta W/\delta J$, and $i\Gamma=W-i\int J\varphi$. With $G_r^c=i^{-r}\delta^rW/\delta J^r$, the response kernel is $\delta\varphi/\delta J=iG_2^c$. Differentiating $\delta\Gamma/\delta\varphi=-J$ once gives the displayed two-point vertex, where the vertex means a derivative of $i\Gamma$. Differentiating the inverse kernel gives the three-point vertex: the connected three-point function is amputated by one inverse two-point kernel on each leg. In the alternative convention $W_c=-i\log Z$, the factors of $i$ are redistributed.