How do electrons couple to gauge field?

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Discussion Overview

The discussion revolves around the coupling of electrons to gauge fields within the context of quantum electrodynamics (QED). Participants explore concepts such as gauge transformations, the role of vector potentials, and the implications for energy levels in quantum systems. The conversation touches on both technical details and philosophical interpretations related to these topics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Meta-discussion

Main Points Raised

  • Some participants question whether the gauge field is different from the vector potential, with at least one asserting that they are not distinct.
  • There is a discussion about gauge symmetry, with some asserting that it involves the transformation of both the vector potential and the phase of the charged particle.
  • One participant suggests that the U(1) symmetry of QED connects states that are physically equivalent, allowing for gauge-fixing to simplify calculations.
  • Concerns are raised about the interpretation of mathematical representations in quantum mechanics, with some arguing that these representations do not necessarily correspond to physical states.
  • Participants discuss the relationship between gauge transformations and energy levels in quantum systems, with one noting that in QED, energy arises from interactions between quantized fields rather than classical potentials.
  • Philosophical implications of the concepts discussed are highlighted, with some participants suggesting that the terminology and interpretations used in quantum theory lead to deeper philosophical questions.
  • One participant expresses a desire to understand the phase factor in relation to interference effects, indicating uncertainty about its implications for particle behavior.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between gauge fields and vector potentials, the nature of gauge symmetry, and the philosophical implications of quantum electrodynamics. There is no consensus on these issues, and the discussion remains unresolved in several areas.

Contextual Notes

Some statements rely on specific interpretations of quantum mechanics and gauge theory, which may not be universally accepted. The discussion includes assumptions about the mathematical representation of quantum states and the implications of gauge transformations that are not fully explored.

Who May Find This Useful

This discussion may be of interest to those studying quantum electrodynamics, gauge theory, or the philosophical implications of quantum mechanics, particularly in relation to particle physics and field theory.

  • #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!
 
Last edited by a moderator:

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