Classical and Field books on symmetries

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Hi.

I am interested in finding books dealing with symmetries.

Specifically books that make me understand assertions like, and I quote Orodruin's #10 and #16 here https://www.physicsforums.com/threa...leaves-the-given-lagrangian-invariant.984601/, 'a rotation in the CoM frame is equivalent to rotation+translation in the original one' or 'boosts and rotations do not commute'.

Besides, and I quote Tong's QFT lecture notes, 'The role of symmetries in field theory is possibly even more important than in particle mechanics. There are Lorentz symmetries, internal symmetries, gauge symmetries, supersymmetries....'

Thus I am also interested in books dealing with symmetries in a QFT context.

What are your suggestions?

Thank you.
 

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Well, if you want to understand symmetries you need first to develop some tools in group theory, so it wouldn't be a bad idea to start with some book in group theory.
Then try to find some book which explains Noether's theorems in every detail.

Now doesn't come any particular book into my mind, if I think of a particularly good book I told you.
 
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vanhees71
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For me one of the most beautiful books introducing symmetries in classical and also somewhat in the very basic beginnings of the quantum field theoretical context is:

R. U. Sexl, H. K. Urbantke, Relativity, Groups, Particles, Springer, Wien (2001).

It covers all important groups as far as the special relativistic spacetime (Minkowski space) is concerned, i.e., translations, rotations, Lorentz, and Poincare groups.
 
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For me one of the most beautiful books introducing symmetries in classical and also somewhat in the very basic beginnings of the quantum field theoretical context is:

R. U. Sexl, H. K. Urbantke, Relativity, Groups, Particles, Springer, Wien (2001).

It covers all important groups as far as the special relativistic spacetime (Minkowski space) is concerned, i.e., translations, rotations, Lorentz, and Poincare groups.
Thank you for the suggestion vanhees71 :)

It looks like a nice book. Unfortunately my uni's library does not have it and it is not available online... 😬
 
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vanhees71
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Well, I have a QFT manuscript at my homepage. Perhaps this helps to start too (though it's much less didactical than Sexl&Urbandtke):

https://itp.uni-frankfurt.de/~hees/publ/lect.pdf

There's a section on Noether's theorem for classical field theories and the long Appendix B on the representation theory of the Poincare group.
 
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Well, I have a QFT manuscript at my homepage. Perhaps this helps to start too (though it's much less didactical than Sexl&Urbandtke):

https://itp.uni-frankfurt.de/~hees/publ/lect.pdf

There's a section on Noether's theorem for classical field theories and the long Appendix B on the representation theory of the Poincare group.

WoW thank you! I am actually following Tong's lectures on youtube, together with his lecture notes. Do you think is a good idea to combine it with your work? (what I mean is if it is at the same level of difficulty).
 
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vanhees71
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For sure it's suitable for the standard lectures on QFT (at my university we have two semesters QFT theory lectures), but it also contains much more formal stuff like the reproduction of Weinberg's proof of his famous theorem. Also Appendix B is not standard for introductory lectures but more specialized. I've once used the parts on renormalization for a special lecture on renormalization theory. The audience of this lecture were mostly advanced undergrad. and grad. students working with QFT methods on their theses.
 
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