Group Theory in a Nutshell for Physicists

After the debut in the textbook series “In a Nutshell”, titled “Quantum Field Theory in a Nutshell” which I enjoyed so much, nearly a decade had passed before A. Zee’s second textbook (on Einstein’s gravity) was released. Then, a few years later, his third - on group theory - came out. From my experience with “QFT in a Nutshell”, I came to realize that group theory is an indispensable tool to understand QFT (and the Standard Model especially), but sadly I wasn’t taught group theory when I was an undergraduate and to me the SO(N), SU(N) were horrible monsters. Motivated by the desire to clear obstacles to learning QFT, I decided to tackle his third book before saying hello to Einstein’s gravity.In view of the impressive achievement of “QFT in a Nutshell”, I have had high expectations on this book. Now that I’ve just read the first several chapters (about one-fourth of the book), but I can say that my expectations are met. This is definitely an ideal textbook on group theory tailored for physics-oriented guys. I’m one of these guys and find it hard to have joy going through textbooks on advanced mathematics in which the narratives are overwhelmed by floods of equations, formulas and mathematical symbols. But in this one, as in “QFT in a Nutshell”, I’m intoxicated by the lively, and sometimes funny, narratives. The mathematics are developed to the physicist's level of rigor, whereas emphasis is put on the connection between group theory and physics. So for those who want to know how the ideas of groups are manifest in the physical world, listen, look no further, your wish would be fulfilled by Zee’s crystal-clear explanation. It is also ideal for self-study, provided the reader has some knowledge of linear algebras and quantum mechanics. Again, the footnotes in each chapter are full of interesting human stories and legends in the history of science, which make the book all the more humanely approachable.The above is my humble opinion based on my partial reading. Therefore the question is: Is it possible that my comment will be different after I have read the whole book? If yes, it would only be more positive. Unless the final parts were not written by the same author. The truth is, “Group Theory in a Nutshell for Physicists” turned me into a big fan of Zee, in much the same way as the film “2001: A Space Odyssey” turned me into a big fan of the director Stanley Kubrick, who made a masterpiece in every different genre of films.Being a big fan of the author, I very much wish that Zee would expand his excellent “In a Nutshell” series.

I just finished reading this wonderful book filled with empowering puzzles. I've never had this much fun with a physics book, myself being at an age of 43, that means something.I started reading this book because I grew frustrated of so many particle physics books slowly explaining the basics of particles in ten chapters, and then at the end the author feels the need to explain the standard model in ten pages and you get one chapter full of deceptively simple looking equations like 9 = 5 + 3 + 1 where quite some readers (like myself) don't really understand what the meaning of these equations are. I studied physics at the university, and we got a course on group theory, but those lectures did not come much further than a couple of finite groups and some playing around with Clebsches, we never saw any tensors there.Zee's book really explains it all really well, you just have to do all the exercises to be able to follow, but when you do (and it is really doable because the exercises are really well balanced - not too simple and not too difficult), you will get a firm and steady grasp on the subject. At the very end of the book, there are some really great exercises (e.g. those where you have to decompose the 126 and the 120 of SO(10), where most of the book's subjects come together. Really lots of fun playing a DIY grand unifier like that. Like the author encourages you to do many times, just do it !Now with physics not being the physics of the eighties anymore, many people are dying to learn more about what the AdS part of AdS/CFT means. With a nice chapter rather early in the book on topology and group (coset) manifolds, you have all the ingredients to understand the essence. This is a modern book on group theory, not afraid to cover many hot research topics of today. Finally infantile looking equations like 15 = 6 + 2 + 3 + 3 + 1 lost their impenetrable mysteriousness. The book made me buy the G nut and the QFT nut as well. Can't wait to devour them!

I own about eight books with titles like group theory in physics, and I took a vow not to buy any others. But when A. Zee writes a physics book (especially in the Nutshell series), I feel compelled to buy it, as he is such a fantastic teacher, and expositor of theoretical physics. I received the book today, and having thumbed through the book it looks like an excellent place for an undergraduate to start his group theory studies. About the only topic that I think is missing is Young tableaux, but these are covered in some of my other books. There seems to be an infinite amount to learn on symmetries and groups in physics, and Zee's book seems like the best beginning book.Having now finished the book, I would like to add some comments. First there are lots of errors, but they are the easy kind to spot - sort of keeps the student on his toes. My favorite concerns the doozy on P.470 on the product of two Feynman slash variables (Wouldn't it be nice if the error were true), but of course where the author uses it, in the following sentence on equating the variables, ends up being correct. Second I wish there were more exercises, particularly in the latter third of the book there are often 1,2, or no exercises per section. Of course as Zee admonishes, he expects you to be actively working out the material in the text even before you read it. But still problems/calculations are essential for both cementing material and applying/extending to new material. And I wish Zee had included more.In terms of content, the book excels at explaining and using the concept of real, pseudo real, and complex representations. No other group theory book (some don't even mention the topic) treats this as well as Zee does. Additionally his treatment of Clifford algebras and spinors is masterful. So if you see QFT, GUTS, Supersymmetry, and or Strings in your future, this book is the easiest place to get some necessary background knowledge, and be entertained as well.