How do electrons couple to gauge field?

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SUMMARY

The discussion centers on the coupling of electrons to gauge fields in Quantum Electrodynamics (QED), specifically addressing gauge transformations involving the vector potential A and the phase factor U. The participants clarify that gauge symmetry involves the joint operation of these elements, and that the interaction between the quantized electron field and the quantized photon field is responsible for energy changes when electrons absorb photons. The Coulomb potential is discussed as a classical representation of interactions, which is replaced by an energy density involving charge densities as operators.

PREREQUISITES
  • Understanding of Quantum Electrodynamics (QED)
  • Familiarity with gauge transformations and U(1) symmetry
  • Knowledge of vector potentials and their role in quantum mechanics
  • Basic concepts of electromagnetic fields and their quantization
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  • Study the implications of U(1) gauge symmetry in QED
  • Learn about the role of the Lagrangian in quantum field theory
  • Explore the concept of gauge-fixing and its applications in electrodynamics
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Physicists, particularly those specializing in quantum mechanics and quantum field theory, as well as students and researchers looking to deepen their understanding of gauge theories and their implications in particle physics.

  • #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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