A Electron Vertex Function in QED

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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 cancelled 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

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

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