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I'll try to be clear. I'd like to ask you if you know some books or chapters in textbooks which explaining the "meaning" of some physical phenomena or entities.

I may try to be more specific using an example to explain what i'm looking for. Let's take electrodynamics: we use both fields and potentials to describe the whole spectrum of electromagnetic phenomena. I have this doubt:

  • which concept is "more real" and fundamental: the field or the potential?

  • Are the potentials just a useful mathematical escamotage?

It may be banal but i don't know the answer. I read that in modern times the vector potential plays a central role in the theory and it is good to build the theory around it, why? "Just" less mathematical complication or a more physical insight? Maybe I never even thought about some interesting question about the fundamental quantities and therefore I'll never look for those answer.

As other example of what I mean I may say I'd like something in the style of the first chapter $1$ of the Feynman vol. $II$, the chapter 19 on the Principle of Least Action, or the chapter on electromagnetic mass in the same book.

Edit: it's not a duplicate. I didn't ask for an undergraduate electrodynamics course. I asked for a book different in the way it explains stuff and not just about EM, but about physics in general. I made the electrodynamical example to explain what I needed. That question thred that has been put here it's of no help


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marked as duplicate by Qmechanic Jul 10 '16 at 12:16

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  • 2
    $\begingroup$ The Aharonov Bohm effect is certainly worth looking into regarding the vector potentials used in E.M. en.m.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect $\endgroup$ – user108787 Jul 9 '16 at 14:15
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    $\begingroup$ escamotage is synonymous with trickery, slight of hand, juggling, just for all you physics focused people. $\endgroup$ – user108787 Jul 9 '16 at 14:18
  • $\begingroup$ I agree completely with you that some textbooks stop at the mathematical and physical aspects of a subject and don't follow through on the consequences and ramifications of the math, but if you do the exercises, or look up Wikipedia, that should help. Also some of the better popsci books do cover the results of math results in more detail. $\endgroup$ – user108787 Jul 9 '16 at 14:42
  • $\begingroup$ Thank you for your answer. I'd like to precise it's not a duplicate. I wasn't asking for books for undergraduate electrodynamics. I was talking about physics in general and I made the electrodynamical example to help understand what I wanted. I don't need an undergraduate physics text. I need something different. The way it has to be different I explained it in the post $\endgroup$ – Run like hell Jul 19 '16 at 8:31

Disclaimer: i understand you didnt ask about gauge invariance but gauge invariance and vector potentials are connected and so ill discuss both in my answer below.

Schwartz "quantum field theory and the standard model" has a good, albeit very brief, accessible discussion of the utility of gauge invariance, in particular the vector potential.

Gauge invariance, i.e. a redundancy in the description of a physical system, is more general than the idea of using vector potentials.

Ultimately we use the vector potential and gauges to aid in computation...gauge invariance has no physically observable effects, however global topological properties of the vector potential DO produce physical phenomena - see Aharonov-Bohm effect.

Other good books that i have found very helpful in understanding these topics are Greiner "quantum mechanics: special chapters" Zee "quantum field theory in a nutshell" and Zangwill "classical electrodynamics" and the excellent book by Landau "classical theory of fields"

Personally i was confused by the need for vector potentials and gauges until i started studying quantum field theory.

In QFT the idea behind gauge invariance becomes much clearer but it can still be confusing.

I hope this helps!


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