Solid State Group theory paper suggestions for my classes

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The discussion centers on teaching group theory to physicists, particularly in the context of condensed matter physics. The instructor currently uses two papers that effectively introduce group theory concepts in relation to physical problems. They seek a third paper that focuses on Lie algebras and continuous groups, ideally a concise text that encourages students to engage with traditional textbooks for deeper understanding. Suggestions include exploring original papers by E. Noether, which are foundational in the field, and considering short essays on SU(2) that provide insights without extensive calculations. Emphasis is placed on the importance of understanding symmetry operations as sub-groups of nuclear permutations, highlighting the relevance of classic papers that are accessible yet informative for students.
Gerson J Ferreira
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I teach group theory for physicists, and I like to teach it following some papers. In general my students work with condensed matter, so I discuss group theory following these papers:


These are great papers to follow, since both discuss group theory superficially as they apply it to interesting physical problems. So, in the class we read these papers and fill the gaps following traditional books (e.g. Tinkham).

Now I'm looking for a 3rd paper to follow in the same manner as above, and introduce an applied discussion over Lie algebras and continuous groups in general. Any suggestions?
 
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thanks! It is a bit long, but seems useful for my purposes.

Ideally, I would like something more like a paper, rather than a book. I mean... a short text that has some interesting developments regarding Lie groups or Lie algebras, but it is not self-contained, thus requiring the students to go for the books to fill the gaps. There are other books with applications and so on, but I find that the students dive deeper in the books when they have to read it to understand another shorter text.
 
Gerson J Ferreira said:
thanks! It is a bit long, but seems useful for my purposes.
You could cut it by chapters.
Ideally, I would like something more like a paper, rather than a book. I mean... a short text that has some interesting developments regarding Lie groups or Lie algebras, but it is not self-contained, thus requiring the students to go for the books to fill the gaps. There are other books with applications and so on, but I find that the students dive deeper in the books when they have to read it to understand another shorter text.
You could give them the original papers of E. Noether. I don't know any translations, but I'm sure there are some on the internet. Hopefully they will have translated the historical language as well for otherwise, this will be an additional difficulty. However, these two papers are the reason Lie groups become famous in physics at all.

Maybe the short essay about SU(2) I wrote as an insight would do:
https://www.physicsforums.com/insights/representations-precision-important/ (about the abuse of language by physicists here)
https://www.physicsforums.com/insights/journey-manifold-su2mathbbc-part/ (about SU(2), 2 parts)
It's not very complicated, but of course doesn't contain the calculations or proofs, which must be done personally, resp. searched in the literature. The second part is a bit more about the Lie algebra, so I'm not sure whether this fits your goal.

I would go with Noether.
 
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What I think is extremely important in a class on group theory in condensed matter is to teach the insight that (almost) all relevant symmetry operations are sub-groups of the symmetry of nuclear permutations. A classic paper which is not too difficult is:
https://www.tandfonline.com/doi/pdf/10.1080/00268976300100501
 
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