QED Formulation with Massive Photon Fields

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Discussion Overview

The discussion revolves around the formulation of Quantum Electrodynamics (QED) using massive photon fields, specifically exploring the implications of treating the photon as a massive vector boson and the associated changes in gauge invariance and propagators. Participants seek to identify the formalism used and request references for further reading on the topic.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that Veltman treats the photon field as a massive vector boson, which alters the propagator and addresses infrared divergences.
  • Another participant suggests the term "Proca" as relevant to this formulation.
  • A different participant mentions "Stückelberg," indicating that he has shown it is possible to have a gauge theory with massive gauge bosons in the Abelian case.
  • There is a request for references that provide detailed discussions on this topic, rather than just brief mentions in textbooks.

Areas of Agreement / Disagreement

Participants present multiple competing views regarding the terminology and frameworks associated with massive photon fields, specifically mentioning both Proca and Stückelberg. The discussion remains unresolved as to which term or framework is more appropriate or widely accepted.

Contextual Notes

There is an indication of uncertainty regarding the appropriate terminology and the depth of available literature on the subject, as well as a reliance on specific interpretations of gauge theories.

Who May Find This Useful

Readers interested in advanced quantum field theory, particularly those exploring alternative formulations of QED and the implications of massive gauge bosons.

M91
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TL;DR
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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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?
 

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