= Scalar Feynman propagator pole prescription
{title2=$\widetilde\Delta_F(p)=i/(p^2-m^2+i0)$}
With $\Delta_F=\langle0|T\{\phi(x)\phi(y)\}|0\rangle$, for a mode of positive <energy> $E>0$ the <Feynman i-epsilon prescription> puts poles $+E-i0$ and $-E+i0$ in opposite half-planes. The <energy> <contour integral> closes clockwise below for positive time separation and counterclockwise above for negative separation. The <residue theorem> gives $e^{-iE|t|}/(2E)$ in either case. Thus the four-dimensional Fourier integral has numerator $i$ and denominator $p^2-m^2+i0$. The integral is understood as a <distribution> limit, not an ordinary absolutely convergent integral; changing the definition to $i\Delta_F$ would change the displayed normalization.
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