Question

Renormalization Point for Coulomb Potential?

Answer 1

1.6*10^19 is remoralization point for columb charge

Answer 2

Hello mate here is your answer.

In this case, for simplicity, we have defined the renormalized charge, eR≡eeff(m)eR≡eeff(m), at Q=mQ=m rather than at Q=0Q=0. (One could also define eReR at Q=0Q=0, as with the Uehling potential; however, then one would need to include the full mmdependence to regulate the m=0m=0singularity.)

This is equally mysterious to me, because in the book Eq. 16.56 that holds for p0=0p0=0 (the equation above), is used directly to derive Eq. 16.65:

e2eff(p):=1+e2R12π2ln(−p2m2).eeff2(p):=1+eR212π2ln⁡(−p2m2).

Nevertheless, he claims that this somehow holds for p0=mp0=m although the equation we started with holds for p0=0

Hope it helps you.