Electron Vertex Function in QED

In summary, the conversation discusses the calculation of the QED electron vertex function and its dependence on two scalar form factors, F1(q^2) and F2(q^2). The book by Peskin and Schroeder only computes F1(q^2) to order α and shows how to deal with infrared divergences. The conversation also mentions that F1(0) is equal to 1 to all orders in perturbation theory, and this is what prevents F1 from playing a role in low energy physical quantities. The g anomaly is due to F2, which has a non-unity value at low energies.
  • #1
Jamister
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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?)
 
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  • #2
I don't know, but please be more specific. In Peskin book where?
 
  • #3
orisomech said:
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.
 
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Related to Electron Vertex Function in QED

What is the Electron Vertex Function in QED?

The Electron Vertex Function in QED (Quantum Electrodynamics) is a mathematical description of the interaction between an electron and a photon. It is used to calculate the probability of an electron emitting or absorbing a photon, and is an important tool in understanding the behavior of particles in quantum field theory.

How is the Electron Vertex Function related to Feynman diagrams?

The Electron Vertex Function is represented by a specific type of Feynman diagram, called a vertex diagram. In these diagrams, the electron and photon are represented by lines, and the vertex function is calculated by summing over all possible diagrams that contribute to the interaction between the two particles.

What is the significance of the Electron Vertex Function in QED calculations?

The Electron Vertex Function is a crucial component in QED calculations, as it allows for the calculation of scattering amplitudes and cross-sections for electron-photon interactions. These calculations are essential in understanding and predicting the behavior of particles in high-energy physics experiments.

How is the Electron Vertex Function affected by quantum corrections?

The Electron Vertex Function is subject to quantum corrections, which take into account the effects of virtual particles in the interaction. These corrections can significantly alter the value of the vertex function and must be taken into consideration in accurate QED calculations.

Can the Electron Vertex Function be extended to other particles?

Yes, the concept of a vertex function can be extended to other particles and interactions, such as the quark-gluon vertex function in quantum chromodynamics. However, the specific form of the function and its calculation will differ depending on the particles involved and the type of interaction being studied.

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