Source differentiation inserts time-ordered field operators (source code)

= Source differentiation inserts time-ordered field operators
{title2=$G_r=\left.i^{-r}\delta^r Z/\delta J(x_1)\cdots\delta J(x_r)\right|_{J=0}$}

A <functional derivative> of the source term in a Minkowski <scalar field path integral> inserts $i\phi(x)$. Time-slicing identifies the resulting product with the <time-ordered product> of field operators. Dividing by the zero-source vacuum functional removes disconnected vacuum diagrams. The normalized formula has one factor $1/i$ for every insertion.