Reversed-frequency scalar contraction (source code)

= Reversed-frequency scalar contraction
{title2=$D_F(z)^*=\int_p\frac{-ie^{-ipz}}{p^2-m^2-i0}$}

With $p\cdot x=Et-\mathbf p\cdot\mathbf x$, placing an annihilation operator on $e^{+ipx}$ rather than $e^{-ipx}$ makes its vacuum time-ordered contraction equal to $D_F^*$, with the opposite pole prescription. For positive time separation, the zero-spatial-momentum factor is $e^{+imt}/(2m)$ rather than $e^{-imt}/(2m)$. Replacing the integration variable $p$ by $-p$ does not change the sign of $i0$ and cannot fix the physical positive-energy boundary condition.