Customer Reviews

Group Theory in Physics

5 star:		(2)
4 star:		(2)
3 star:		(1)
2 star:		(1)
1 star:		(0)

 

 

This book gives an excellent introduction into group theory and provides a working knowledge for those who want to study field theory (for example). I especially like the complete treatment of representations of the classical groups and the Lorentz and Poincare groups.

This is not a bad book. The contents are comprehensive. The theorems are well proved. Graphs are used appropriatly to clarify the concept. But it has several shortcomings. One is the line space is too small, too many words are clustered together. Another is sometimes the proofs are too short. Some explanation should be given on certain points because those points are not so obvious and should not be taken for granted. Frankly, I love group theory, but after reading this book for 20 pages, I felt very tired, both because of the bad format and hard thinking. Hamermesh's book will give you a more enjoyable reading.

I like this book. I got it after struggling with some books on quantum field theory and finding myself unable to answer basic self-asked questions like "what is a spinor?". I went through the first 8 chapters and will go back and finish it some day. It's almost all math, very few explicit physics applications (apart from an interesting introduction in Chapter 1) which seems to upset some of the other reviewers, but I enjoyed it anyway. Group theory is beautiful and logical, and Professor Tung's exposition is concise and elegant. He doesn't waste any words and the notation is dense, which also seems to upset some of the other reviewers, but hey, that's math for you. If you would like to learn the essentials of the groups used in physics, this book will do the trick. You can then go back to the physics books for the applications.

P.S. I was only able to find a single typo!

I got to this book at a time when I was interested in a presentation of the method of induced representations, of fundamental importance for quantum physics because it allows a systematical derivation of the fields consistent with a given Lie group, so that it is of basic importance for quantum field theory. After a lot of search through books on group theory I found this method very clearly presented here in Wu-Ki Tung's book, and then I started to study it thoroughly, following it with pen and paper. Of course, I went through many other parts of this book, and I found it excellently written by a person who loves this subject and who strived and succeeded to patiently present it all, gradually, from simple to complex and in a very clear and coherent exposition from beginning to end. I am delighted by it. It was very useful to me. By the way, I was directed to this book by the bibliography given in a chapter of the outstanding The Quantum Theory of Fields, Volume 1: Foundations by Steven Weinberg.

Wu-Ki Tung's book is recommended by Weinberg's famous textbook The Quantum Theory of Fields, Volume 1: Foundations, and does indeed have a useful treatment of Lorentz transformations and angular momentum. I found the preliminary part of the book that constitutes chapters 1-6, however, hard to follow, with proofs that were too cryptic for me to understand. So for these early chapters the reader might do better to get the basic understanding of group theory from Tinkham's book Group Theory and Quantum Mechanics.

One brief section in this book that I particularly liked was the discussion of doubly connected curves, a concept that I had encountered in other books, but did not understand. On pp.96-97 Tung provides a good example of this concept, as illustrated in Fig.7.2. I have included jpeg files for these pages in this review.

It is difficult to fathom how someone could write a 350+ page book on group theory for physicists in 1985, which contains almost nothing addressing the most important applications of group theory in the last half century. Hello, ever hear of the Standard Model? Grand Unification? It's like this book was written in the 1950s; it goes on and on about SO(3) and the lorentz group, etc. Special unitary groups are only mentioned in passing. Not even a hint of the exceptional groups. Georgi's book has what physicists actually need in a small fraction of the page count.