How do electrons couple to gauge field?

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In quantum electrodynamics (QED), the coupling of electrons to the gauge field involves gauge transformations that affect both the vector potential and the phase of charged particles. The U(1) gauge symmetry is fundamental, linking the photon field and the electron field, and allows for the mathematical formulation of interactions without altering physical states. The energy of an electron is influenced by its interactions with the quantized photon field, particularly when photons are absorbed, leading to changes in energy levels. The discussion also touches on the philosophical implications of these concepts, emphasizing the need for a clear understanding of the underlying mathematics and its relation to physical phenomena. Overall, the interaction between electrons and photons encompasses both gauge symmetry and energy exchange processes.
  • #31
Furthermore, I don't see how the Ward-Takahashi identities have any impact on the form of the original QED Lagrangian.
 
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  • #32
Polyrhythmic said:
Furthermore, I don't see how the Ward-Takahashi identities have any impact on the form of the original QED Lagrangian.

You should familiarize yourself with renormalization.
 
  • #33
Dickfore said:
You should familiarize yourself with renormalization.

I'm familiar with renormalization, that's why I wrote "original" instead of "renormalized" Lagrangian.
 
  • #34
Polyrhythmic said:
I'm familiar with renormalization, that's why I wrote "original" instead of "renormalized" Lagrangian.

If you really understood the gist of Renormalization, you would know that the "original" Lagrangian is not connected to reality.
 
  • #35
I understand that. Apparently we were both confused with what the other one meant! ;)
 
  • #36
Polyrhythmic said:
I understand that. Apparently we were both confused with what the other one meant! ;)

Actually, my comments started as a reply to OP's https://www.physicsforums.com/showpost.php?p=3491614&postcount=25" where he mentions "Proca Lagrangian". I don't know what your intention was or whatever it was that you had in mind.
 
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  • #37
Dickfore said:
Actually, my comments started as a reply to OP's https://www.physicsforums.com/showpost.php?p=3491614&postcount=25" where he mentions "Proca Lagrangian". I don't know what your intention was or whatever it was that you had in mind.

I see, now everything is clear to me, I didn't realize you were talking about Proca theory. Sorry for the confusion!
 
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