I am reading a very nice Physics book "The standard model in a nutshell" by D.Goldberg and just read there a mention to Noether Theorem. Of course I knew this outstanding theorem very well from previous physics courses : "A symmetry in the system (Lagrangian) implies a conserved physical quantity". The proof is quite short it follows from the Euler Lagrange equation and a few lines of calculus. But now that I think about it, I am not that happy with it. I fell like such a important result should have a more abstract and geometrical understanding. Do you know another proof of Noether Theorem written in a differential geometry setting and that can be generalized in a more abstract case?
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2$\begingroup$ You'll find a quick proof of Noether's theorem, in greater generality than you're likely to need even, in this recent answer. $\endgroup$– Igor KhavkineCommented May 4, 2020 at 16:28
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$\begingroup$ I suppose the proof in section 2.3.1 of this article arxiv.org/pdf/1601.03616.pdf are those few line of calculus. But maybe not, you can glance it $\endgroup$– Gabriel PalauCommented May 4, 2020 at 16:28
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$\begingroup$ Khavkine's answer is really excellent. $\endgroup$– Ben McKayCommented May 4, 2020 at 16:49
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$\begingroup$ You may also be interested in the discussion here: physics.stackexchange.com/questions/19847/… $\endgroup$– Phil TostesonCommented May 4, 2020 at 18:49
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