= Gaussian evaluation of a free scalar generating functional
{c}
{title2=$Z_0[J]=\exp[-\tfrac12\int J\Delta_FJ]$}
Completing the square in the free scalar <path integral> gives a quadratic exponential in the source. If $\Delta_F$ includes the factor $i$ in the momentum-space <Feynman propagator>, the normalized Minkowski functional is $\exp[-\int J\Delta_FJ/2]$. Two source derivatives with their $1/i^2$ factor recover $\Delta_F$, while higher derivatives give <Wick contractions>.
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