Propagator kernels in a positive-sign Gaussian generating functional ($D=-i\Delta ,F=-iS$)

With source term $J\varphi +\bar{\eta }\psi +\bar{\psi }\eta$ and left functional derivatives, a free functional written as $Z_0\propto \exp (iJ\Delta J/2+i\bar{\eta }S\eta )$ has physical time-ordered contractions $D=-i\Delta$ and $F=-iS$. The kernels in this exponent must not be identified with contractions already carrying factors of $i$. Four contractions in a second-order Yukawa scalar two-point graph introduce $(-i{)}^4=1$, leaving its kernel formula's overall coefficient unchanged.