Group Theory in Physics: An Introduction to Symmetry Principles, Group Representations, and Special Functions in Classical and Quantum Physics

Others have noted, one reason to peruse this publication is that Steven Weinberg refers to it in his volume one, Quantum Theory of Fields (1995, page 68): "unitary representations can be broken up into a direct sum of irreducible unitary representations." Based upon Weinberg's recommendation, turn to Tung: sections #7.3 and #8.1. Section 7.3 is entitled "Irreducible representations of SO(3) and Lie Algebra" and section 8.1 describes the relationship between SO(3) and SU(2). Weinberg also refers to Tung in his Cosmology text (page 374). Now, if Steven Weinberg's recommendation is insufficient to prod your interest, then this textbook is not for you.(1) I do highlight a sentence from the preface: "this book is also designed to be used for self-study." That is a difficult goal to fulfill. I believe the author succeeds in that goal. While the exercises do not include complete answers, they are (in many cases) accompanied by hints at how to arrive at the answer.(2) It is true that you will not get applications to topics such as grand unification (always a dubious enterprise). Thus, little duplication of such things that are found in Georgi's book (first edition). Reading Tung: "the material we have covered should provide adequate background and concrete experience for the reader to explore both the more general mathematical theory and the diverse physical applications." (page 290). Therefore, I suggest perusing Tung previous to perusing Howard Georgi (his first edition, 1982).(3) Tung eschews discussion of crystal lattices. If you desire that, Morton Hamermesh is a great place to get it. Also, quite enlightening on that topic is the excellent book by Sternberg: Group Theory and Physics (1994).(4) Some exercises here can be found in other books, for instance: "Consider the dihedral group, which is the symmetry group of the square...enumerate the group elements, the classes, the subgroups, the factor groups..." (#2.8, page 26). If you need the correct answer, you can locate the answer in a number sources. Howard Georgi, as an exercise, asks the student "to prove Schur's lemma." If you can prove Schur's lemma on your own, after study of his previous fourteen pages of Georgi (1982), then you do not need Tung. Mere mortals, however, turn to Tung who expounds upon it (with proof, pages 37 and 38).(5) I provide another example which can be found elsewhere: "We apply the group-theoretical notions to a familiar system, a single particle in a central potential. We shall see that a number of important results can be inferred from symmetry considerations..." (page 110). Now, exercise #7.3 (page 124) reads: "from geometrical considerations, derive the following result which describes the effect of the rotation on an arbitrary vector..." Sattinger and Weaver, in their exercise #5 (page 15), Lie Groups and Algebras with Applications, ask the reader to "...prove..." that same formula in different guise. This brings up another point: Tung's is a physicist's approach, pitched to a more physical approach and Sattinger and Weaver is pitched to a mathematically mature audience. Morton Hamermesh (elementary) and Eugene Wigner (advanced) are also physically inclined expositions.(6) A few highlights: Tung works-out the details, in considerable detail ! Almost all intermediate steps are kept in plain sight (example: Young diagrams, not at all mysterious here, chapter five). An instance where Tung has made his mark: relation between representations of the Lorentz and Poincare groups, relativistic wave functions, fields and wave equations (pages 202-209).(7) Concluding my review (although, I have barely scratched the surface of this textbook), Tung really does satisfy the needs of the self-study student. Tung serves as springboard to advanced material. If Steven Weinberg points to this book as reference, one does best not to ignore his advice.Highly recommended textbook !Physics Today: Wu-Ki Tung, " among the most influential theoretical high-energy physicists of his generation,"died on March 30th, 2009.

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!

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.

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.

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.

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.

Ottimo servizio di Amazon, il libro è arrivato puntuale, in condizioni perfette.E' un ottimo libro, ben strutturato e rispetta in pieno "in Physics" in quanto veramente destinato ad uno studente di Fisica.Consigliato sia per una laurea triennale che per studi successivi.

Gostei demais do livro. Linguagem acessível e profunda.

This is the best book one can get for group theory.