- #1

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I found one article in 1993 talking about it.

**[Unacceptable reference deleted by the Mentors]**
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- Thread starter timeant
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In summary, the conversation discusses the derivation of Maxwell's equations from gauge symmetry and charge conservation. There is disagreement about the validity of certain publications and the role of gauge symmetry in deriving conservation laws. The thread is eventually closed due to high moderation and potential bias from one of the participants.

- #1

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I found one article in 1993 talking about it.

**[Unacceptable reference deleted by the Mentors]**

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- #2

Mentor

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- #3

Mentor

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This is my favourite one:

https://iopscience.iop.org/article/10.1088/0143-0807/36/6/065036/pdf

There is a bit more that can be said about the derivation regarding where that e comes from but will leave it there at the moment. It becomes clearer when you see the derivation from Guage symmetry:

https://quantummechanics.ucsd.edu/ph130a/130_notes/node296.html

But it is well known the fundamental basis of EM is gauge symmetry. Noether's Theorem basically says symmetry leads to a conservation law and conversely. The conservation law from gauge symmetry is charge conservation, so it is hardly surprising that it also leads to Maxwell's equations. I have seen several 'derivations', and they all really boil down to gauge symmetry or charge conservation - plus relativity, of course.

Thanks

Bill

https://iopscience.iop.org/article/10.1088/0143-0807/36/6/065036/pdf

There is a bit more that can be said about the derivation regarding where that e comes from but will leave it there at the moment. It becomes clearer when you see the derivation from Guage symmetry:

https://quantummechanics.ucsd.edu/ph130a/130_notes/node296.html

But it is well known the fundamental basis of EM is gauge symmetry. Noether's Theorem basically says symmetry leads to a conservation law and conversely. The conservation law from gauge symmetry is charge conservation, so it is hardly surprising that it also leads to Maxwell's equations. I have seen several 'derivations', and they all really boil down to gauge symmetry or charge conservation - plus relativity, of course.

Thanks

Bill

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- #4

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The electric charge (or the electric-charge four-current) conservation follows from the corresponding global symmetry and is a necessary condition for the consistency of the gauge theory. For details see

https://www.osti.gov/servlets/purl/6129984/ (preprint)

https://doi.org/10.1119/1.16219 (paper)

- #5

Mentor

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Are those spam links at the end of the PDF paper that you linked to? What are those? They look misplaced in a scientific publication...

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- #6

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berkeman said:Are those spam links at the end of the PDF paper that you linked to? What are those? They look misplaced in a scientific publication...

https://www.physicsforums.com/attachments/283358

Yes, it is an issue that needs to be sorted out. We do not promote 'spam' here.

Thanks

Bill

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EM gauge symmetry leads to conservervation laws having no physical meaning.

**Electric charge **conservation law can be derived from **Dirac **field's gauge symmetry by Noether theorem, not by EM field.

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- #9

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It can be derived from the global symmetry not from the local one. That's a subtle point and one should think it through carefully. See the AJP paper quoted in #4.timeant said:EM gauge symmetry does not lead to conservervation laws having no physical meaning.

Chargeconservation law can be derived fromDiracfield's gauge symmetry by Noether theorem, not by EM field.

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Free EM fields are built up by ##A_{\mu}##. Electric charge density and current, which is irrelevant ##A_\mu##, are built by Dirac's ##\psi##.vanhees71 said:It can be derived from the global symmetry not from the local one. That's a subtle point and one should think it through carefully. See the AJP paper quoted in #4.

I think you all should care about the academics, not the useless links.

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Thread is closed for Moderation...timeant said:I think you all should care about the academics, not the useless links.

- #12

Mentor

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- #13

Staff Emeritus

Science Advisor

Education Advisor

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(1) If it's a scientific paper, it doesn't have spam in it. Full stop.

(2) I don't believe you are here to ask questions. I believe you are here to push your own point of view. That's based on what you have written in this and other threads.

(3) That makes (1) even stronger. BTW, did you write it?

(4) To answer your original question, "The back way for deriving Maxwell's Equations: from charge conservation?", you can't. There are other theories with charge conservation that have different "Maxwell Equations" - Proca Electrodynamics and Calssical Yang-Miles to name but two.

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Thread closed.

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