QED Formulation with Massive Photon Fields

In summary, the conversation discusses the formulation of QED using the Proca formalism, which allows for the treatment of IR divergences. The topic is also mentioned in Weinberg's book, but the conversation suggests finding a more detailed reference on the subject.
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M91
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TL;DR Summary
Massive QED formalism.
I was reading Diagrammatica by Veltman and he treats the photon field as a massive vector boson in which gauge invariance is disappeared and the propagator has a different expression than in massless photon. After some googling, I found that this is one way to formulate QED which has the advantage of taking care of IR divergences. I would like to read more about the subject. What is the name of such formalism? is there any kind of QFT book (article, paper..) which explains it in detail? I saw some comments in Weinberg's book but Weinberg is too technical for me. Any sources would be appreciated.
 
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  • #2
The word you want is "Proca".
 
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or rather Stückelberg, who has shown that for the Abelian case you can have a gauge theory with massive gauge bosons.
 
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vanhees71 said:
or rather Stückelberg, who has shown that for the Abelian case you can have a gauge theory with massive gauge bosons.
Thanks! I was hoping to get an answer from you, as you always put me in the right direction. Do you also happen to know a reference that discusses this topic in detail rather than books only highlighting this mechanism?
 

1. What is the QED formulation with massive photon fields?

The QED (Quantum Electrodynamics) formulation with massive photon fields is a theoretical framework that describes the interactions between charged particles and electromagnetic fields. It extends the original QED formulation, which only considers massless photons, to include massive photons. This allows for a more accurate description of certain physical phenomena, such as the behavior of electrons in superconductors.

2. How does the QED formulation with massive photon fields differ from the original QED formulation?

The main difference between the two formulations is the inclusion of massive photons in the QED formulation with massive photon fields. This means that the mass of the photon is no longer assumed to be zero, and its effects on particle interactions are taken into account. This allows for a more complete and accurate description of certain physical phenomena.

3. What are the implications of including massive photons in the QED formulation?

The inclusion of massive photons in the QED formulation has important implications for the behavior of charged particles in certain situations. For example, it can explain the behavior of electrons in superconductors, where the presence of massive photons leads to the formation of Cooper pairs and the phenomenon of superconductivity.

4. How is the QED formulation with massive photon fields tested and validated?

The QED formulation with massive photon fields is tested and validated through a combination of theoretical calculations and experimental observations. The predictions of the theory are compared to experimental results, and if they match, it provides evidence for the validity of the formulation. Additionally, the theory is constantly refined and improved based on new experimental data.

5. Are there any limitations to the QED formulation with massive photon fields?

Like any scientific theory, the QED formulation with massive photon fields has its limitations. It is a highly complex and mathematical framework, and its predictions may not always match experimental results perfectly. Additionally, it does not take into account other fundamental forces, such as the strong and weak nuclear forces, which are described by other theories. However, the QED formulation with massive photon fields remains a powerful and widely accepted framework for understanding the behavior of charged particles and electromagnetic fields.

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