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.


Some good options:

  • Symmetries by Griffiths has a nice language and it's mathematically clear, but is oriented to particle physics.
  • Symmetry by Roy McWeeny (Dover) is introductory to Group Theory and its applications to physics (beyond particles). It's a little old, but it's useful.
  • Geometry, Topology and Physics by Nakahara is a good option. 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.
  • Gelfand and Fomin's Calculus of Variations (Dover) has the best explanation of Noether's theorem around, makes it look so obvious. 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.
  • If you'd like videos to accompany you there are NPTEL videos following Elsgolts' Calculus of Variations book which is similar (but not as good) as Gelfand. If you have trouble with the early sections of Gelfand, or would just like a second perspective, those videos would be a great free resource. Unfortunately they don't cover Noether, but the'd help with the CoV pre-req's to get to Noether.

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