As far as I know, absorbing of the positive coefficient of $i\epsilon$ in a propagator seems to be a trivial operation without even the need of justification.

In Peskin page 286, he did this:
$$k^0\rightarrow k^0(1+i\epsilon)$$
$$(k^2-m^2)\rightarrow (k^2-m^2+i\epsilon)$$

In M. Srednicki's Quantum Field Theory, page 51,

The factor in large parentheses is equal to $E^2-\omega^2+i(E^2+\omega^2)\epsilon$, and **we can absorb** the positive coefficient in to $\epsilon$ to get $E^2-\omega^2+i\epsilon$.

Why and does this kind of manipulation affect the final result of calculation?

Although $\frac{1}{k^2-m^2+i\epsilon k^2}-\frac{1}{k^2-m^2+i\epsilon}$ is infinitesimal, but the integration of such terms may lead to divergences, and this is my worry.

Also the presence of $k^0$ in the coefficient of $i\epsilon$ could potentially influence the poles of an integrand and consequently influence the validity of Wick Rotation.

This post imported from StackExchange Physics at 2014-05-04 11:30 (UCT), posted by SE-user LYg