Groups, Representations and Physics 1st Edition

It is very customary for a physicist that when he wants to understand the role of group theory in physics, he has to go a very long way before he is ready to answer a physical question using the newly learnt tools of group theory. This book howeverhas a more straight-forward approach allowing you to both comprehend almost all the formal aspects of group theory and solve specific problems in physics. Besides the book uses a very simple notation and many illustrative examples, which is ussually a great flaw in almost all of the classical texts (Hamermesh's, Weyl's and Wigner's ). Finally, the book is self-contained and leads, without elaborated mathematics (or which is even better, with the virtue of not making it look complicated), to the applications and the problem-solving strategy.

This book sucks. My professor chose it because it covers both lie and point groups, and includes special unitary groups, but when I talked to him about not liking the book, even he agreed that it was a poor choice. The wording is hard to follow and the examples are incomplete. It doesn't go through proofs rigorously. I've had to refer numerous times to other books for clarification.  Group Theory and Its Application to Physical Problems (Dover Books on Physics and Chemistry)  is much better.

I read this book many years ago when I was an undergraduate student because the lecturer recommended the book. However, I had struggled very hard to understand it but somehow I managed to pass the course. Now I am a lecture and re-read this book again and understand why I did not understand before.The author did not explicitly explain the convention for transformation whether it is an active transformation or passive transformation; this is crucial for observant readers because it completely change the point of view or even the composition law. Many of the algebraic rules are left unexplained in enough details which leave the readers to figure out themselves. Besides, I found one of the answer to problems is wrong without any errata to be found on internet. Seriously, this is the second edition already but there is an obvious mistake left in solution to exercises.I would not recommend this book for your first reading at all. The reason I give 2 stars instead of 1 is that the book actually covers everything I want to know about applications of group theory in physics just by looking at the contents. The book could be my favorite if it was well written...

At first glance, this book is accessible and well-written. This is an illusion. In this book, Jones tries to cover the theory of finite and continuous groups, representation theory, lie groups and algebras and applications to quantum mechanics, molecular vibrations, special relativity etc. In doing this, he tries not to confuse the reader with too many mathematical details, seeking instead introduce physical ideas quickly. This is in principle a sound idea, but Jones' implementation is abysmally poor. In particular, he often uses terms he does not define and abuses the notation he does define, even in theorems. (The fact that he doesn't prove many theorems makes it harder to work out the meanings of terms from context.) Even worse, there are often theorem-like statements in the text that are not even pointed to as such, but merely mentioned in passing. E.g. 'You don't need to know what a compact group is, just that the last equals sign is OK because the group is compact' (paraphrased) Many of his examples fail to illuminate the principles he is trying to explain and have the flavour of my students' homeworks when they have copied their answers from the back of the book. E.g. 'The answer is 2+1=3' (paraphased). All right, and whence the 2 and 1?I had taken a basic course in groups based on Armstrong's Symmetry and Groups (which I heartily recommend for a first pass at the subject, although a book on algebra in general might be better) and was reading Jones together with some classmates (post-grads) in the physics department. We spent altogether too much time trying to guess what Jones was trying to say and after that, trying to believe what we thought he said. In the end, after ploughing through six chapters of this book and feeling like Alice in believing more and more impossible things every day (paraphrase! :-) ), I decided to take the long road via 'real maths' books. I'm going through James and Liebeck at the moment, which so far has been a breath of fresh air compared to Jones. After that, Isaacs's book on representations and Humpreys' and Adams's on lie groups and algebras have been recommended to me. It may be of course that there are other physicists who do a better job than Jones. I hear that the books by Cornwell and Wu-Ki Tung are better than Jones', but have not looked at them in too much detail. Perhaps other reviewers will have suggestions.

I have known something about Lie groups and Lie algebras (I have already read first 5 chapters of "Lie Groups, Lie Algebras, and Representations" by Brian C. Hall ) and wanted to combine it with the applications in physics. When I encounter this book, I looked at its content, I thought that I should read it to understand the relation between group theory and physics. But it disappointed me for the following reasons:(1) It lacks of mathematical precision when it is really needed. (There is even a uncomplete definition eg. "reducible representation" on page 45).(2) The relations between physics and representation theory is not directly presented. I have passed hard days to understand the relations and finally read this topics from other books.Therefore, it is very hard to study this book without a teacher. If you will study this subject alone, it is good to begin with the lecture notes (maybe I should say book) by Dimitry Vvedensky at [...]

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Book was in perfect condition, as expected.