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I have a question about the divergence of forward Coulomb (Bhabha/Moller) scattering.

I guess the classical analog of it is the Rutherford cross-section divergence, but that can be explained by the infinite impact parameter.

In the QED version - the Bhabha/Moller scattering, it is the matrix element for given states that diverges - not only the cross-section, and I can't see how two plane-wave particles can have an impact parameter that could resolve this divergence.

Also, it seems that the divergence stems from the zero-momentum divergent photon propagator here. I saw explanations that this is typical for any infinite range interaction.

Could somebody please explain what is the solution for this divergence. Is this an unphysical one? What was the wrong assumption that caused it?

Zero-energy propagator probably means infinite-lifetime virtual photon. Does this has anything to do with the divergence?

http://en.wikipedia.org/wiki/Bhabha_scattering

Coulomb interaction between 2 charged particles is about the 1st thing we learn in high-school after the Newton laws. Doesn't this bother anyone? Am I missing something here?

Thank you.

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# Divergence of forward Coulomb scattering?

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