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What's a good book (or other resource) for an advanced undergraduate/early graduate student to learn about symmetry, conservation laws and Noether's theorems?

Neuenschwander's book has a scary review that makes me wary of it, but something like it would be great.

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Gelfand's Calculus of Variations has the best explanation of Noether's theorem I've ever found, makes it look so obvious. –  bolbteppa Feb 12 at 0:57
I think I already have Lanczos' book on the calculus of variations somewhere in my library. How's that in comparison to Gelfand? (i.e. should I get Gelfand regardless, or be happy that I have Lanczos?) –  user38621 Feb 12 at 1:21
@bolbteppa the above message was for you ^ –  user38621 Feb 12 at 1:33
The thing about Gelfand is that he defines an invariant transformation, gives two explicit numerical examples of these with respect to Lagrangians as a means to motivate Noether, proves Noether - but once you read it you realize Gelfand already taught the general case to you, then gives another numerical example which just so happens to allow for an interpretation as conservation of energy, something he'd already proven a few sections earlier, then does the other conservation laws (something Landau does in another way btw). Later in the book he proves the field-theoretic Noether + examples, –  bolbteppa Feb 12 at 1:45
Lanczos really doesn't compare, having had a quick glance at the appendix on it I know it would have confused the hell out of me, as every explanation of Noether I'd tried to read for more than half a year did, if I hadn't read Gelfand, but of course people are different so it might be a good idea to have a glance at the appendix version. Another way of looking at Noether (in special cases) is Ch. 2 of Landau Vol. 1, I'd say the goal is to try to merge Landau's, Gelfand's, Lanczos' & Goldstein's explanations of Noether (though Gelfand & Landau are the best & all that's needed really). –  bolbteppa Feb 12 at 1:50

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I recommend you "Symmetries" by Griffiths, or "Symmetry" by Roy McWeeny (it's a Dover book). "Geometry, Topology and Physics" by Nakahara is a good option.

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Thanks! Could you also write a little as to why each of your recommendations would be well suited as an answer to my question? –  user38621 Feb 12 at 2:15
Of course! Symmetries has a nice language and it's mathematically clear, but is oriented to particle physics. McWeeny's book is introductory to Group Theory and its applications to physics (beyond particles). It's a little old, but it's useful. Nakahara's book is the basics of mathematics that any theoretical physicist should know. Besides, most of the discussions start from physical applications (QM, SUSY, Strings,and more), without neglecting the mathematical approximations. –  Mike Martin Feb 12 at 6:51

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