Good alternatives to Georgi's Lie Algebras in Particle Physics? [duplicate]

Question

I just started reading Lie Algebras in Particle Physics by Howard Georgi and I'm finding it frustratingly fuzzy. What I mean is that he often makes non-trivial statements without proof, is imprecise with definitions, and so on. However, what other books I can find seem to swing a bit too far the other way, and I simply don't have time for the most comprehensive and rigorous treatments.

The ideal book would be somewhere in the middle. It should be a quick read, but prove or sufficiently motivate important statements. And it should cover the essentials needed in introductory theoretical particle physics; i.e. basic representation theory, basic Lie theory, and something about $SU(2)$ and $SU(3)$. Are there any good alternatives?

Answer 1

Here are some group theory references with a focus on particle physics, basically transcribed from the introduction of my group theory notes.

• Nick Dorey's Symmetries, Fields, and Particles lectures as transcribed by Josh Kirklin. Introduces Lie algebras and Lie groups and outlines the Cartan classification. Rather brief, but covers the essentials for particle physics with a reasonable amount of mathematical precision.
• Georgi, Lie Algebras in Particle Physics. The classic text for particle physicists. This thin book crams lots of content into its 300 pages, squeezing the Cartan classification into just 5, and gives many practical algorithms, at the cost of basically omitting all proofs. The emphasis is on grand unified theories; finite groups receive little coverage.
• Zee, Group Theory in a Nutshell for Physicists. A very readable and easygoing book developing group theory by example, spending significant time on finite groups and applications in quantum mechanics. This is a good first book. It covers a lot of the same content as Georgi, along with some applications to other fields of physics. It is not mathematically rigorous by any means, but it sketches derivations for everything it uses, while Georgi omits even the sketches. It has lots of jokes and lots of typos, but the typos are all the kind that are easy to fix if you're paying attention.
• Wu-Ki Tung, Group Theory in Physics. A methodical group theory textbook that clearly covers the material that no introductory book teaches, but every advanced book assumes you already know, such as Wigner's classification, the Wigner-Eckart theorem, and Young tableaux. More rigorous and formal than most group theory books for physicists (for instance, results as organized into numbered theorems with detailed proofs), but still extremely readable and a great introduction. It ends with a chapter that is extremely useful for understanding the conceptual basis of quantum field theory, but stops short of applications like grand unification.
• Sternberg, Group Theory and Physics. A classic book that focuses on applications in quantum mechanics. It expects more mathematical background, using differential geometry and bundles freely throughout.
• Ramond, Group Theory. A short, clean book which also briefly covers topics of mathematical interest, such as Kac-Moody algebras. Not a good first introduction; better for a fun second look. Beware: the reference tables in the appendix contain a number of mistakes.
• Kirillov, An Introduction to Lie Groups and Lie Algebras. A standard introductory graduate math textbook for Lie theory. Written in the pure math style, but still relatively informal.
• Fuchs and Schweigert, Symmetries, Lie Algebras, and Representations. Covers the standard material rigorously and goes far beyond; a useful reference for theoretical work.

If you don't have time to read a full book, I recommend Dorey's lecture notes. If you want to read something that covers the content of Georgi's book, but with more derivations, I suggest looking at both Zee and Wu-Ki Tung and seeing which you like better.