Electron Vertex Function in QED

[Jamister]

TL;DR Summary

Form Factors Of QED electron vertex function.

In Peskin book they calculate the QED Vertex Function named Gamma which depend on two scalar functions called form factors F1(q^2), F2(q^2).
they are calculating F1(q^2) and they do not really finish calculating for what I understand. They are just showing the Infrared divergent is canceled by soft photons. Does it depend on the energy E_l of the largest energy measurable photon? and according to Wikipedia F1[0]=1 to all orders in perturbation theory , why is that?
And also, are there any physical quantities that are calculated due to F1[q^2] (I guess probably there are high energy physical quantities, but are there low energy ones such as g the anomalous magnetic moment?)

 

[haushofer]

I don't know, but please be more specific. In Peskin book where?

 

[Gaussian97]

Summary: Form Factors Of QED electron vertex function.

In Peskin book they calculate the QED Vertex Function named Gamma which depend on two scalar functions called form factors F1(q^2), F2(q^2).
they are calculating F1(q^2) and they do not really finish calculating for what I understand. They are just showing the Infrared divergent is canceled by soft photons. Does it depend on the energy E_l of the largest energy measurable photon? and according to Wikipedia F1[0]=1 to all orders in perturbation theory , why is that?
And also, are there any physical quantities that are calculated due to F1[q^2] (I guess probably there are high energy physical quantities, but are there low energy ones such as g the anomalous magnetic moment?)

Well, I think in Peskin and Schroeder they simply compute $F_1(q^2)$ to order $\alpha$ and they use that to show how to deal with infrared divergences, if you want a full order calculation of $F_1(q^2)$ then you should look somewhere else.
In Peskin's book, they give you an argument of why $F_1(0)=1$ to all orders if we want to recover Coulombs limit, and they prove it more formally in the next Chapter.
Is just this argument that $F_1(0)=1$ what forbids $F_1$ to play a role in low energy physical magnitudes. The g anomaly is due to $F_2$ which precisely have a non-unity value at low energies.