Reference request: representation focused view of quantum mechanics

Question

I'm interested in learning a bit more about quantum mechanics from a more Lie algebra/representation theoretic perspective, hopefully including but not going past quantum field theory.

I was wondering if there are standard or hidden gem references for this perspective. Things that are publicly available are preferred, but not required. Thank you!

Answer 1

I really like Linearity, Symmetry, and Prediction in the Hydrogen Atom. It's a clear and thorough description of what the representation theory of $SO(3)$ and $SO(4)$ have to do with the structure of the periodic table, which in my opinion is both a really beautiful and a relatively unknown topic.

Answer 2

Peter Woit wrote a book, freely available online.

He himself describes the book on his blog as

The book is based on a year-long course that I’ve taught twice, based on the concept of starting out assuming little but calculus and linear algebra, and developing simultaneously basic ideas about quantum mechanics and representation theory... By the end, the idea is to bring the reader to the point of having some appreciation of the main elements of the Standard Model, from a perspective emphasizing the representation theory structures that appear.

which seems just the type of background that you want.

A review from Inference magazine recommends it too.

Answer 3

$1$. Quantum Mechnics: Symmetries by Walter Greiner & Berndt Muller.

It's about the general theory of Lie groups, the isospin group, hypercharge, $\text{SU}(3)$ symmetry and so on.

$2$. Lie Algebras in Particle Physics - From Isospin to Unified Theories by Howard Georgi.