Group theory paper suggestions for my classes

[Gerson J Ferreira]

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:

[1] Group Theory and Normal Modes, American Journal of Physics 36, 529 (1968)
[2] Nonsymmorphic Symmetries and Their Consequences (unpublished report for a MIT class)​

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?

 

[fresh_42]

I'm not sure whether this isn't too long, but maybe you are looking for something like this:
http://www.staff.science.uu.nl/~hooft101/lectures/lieg07.pdf
It doesn't have a lot about Lie algebras, but as we are in group theory, this shouldn't be a disadvantage.

 

[Gerson J Ferreira]

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.

 

[fresh_42]

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.

 

[DrDu]

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