Customer Reviews

Group Theory and Its Application to Physical Problems (Dover Books on Physics)

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When I first encountered this book I was an undergrad, a junior. I flipped through the pages and could barely read the English portions, not to mention the proofs and examples. I must say that it's a tough book for a beginner; MH quickly runs through group theory in the beginning (pay attention: there are some important sentences in there that pop up later when you least expect them to) and then goes into rather a lengthy description of symmetry (point) groups, fit for a chemist or crystallographer more than a theoretical physicist.

After those two chapters come perhaps the most important chapters in the book: the ones on group representation theory. There is a long chapter on theory, and then a great short one on applications of GR that's extremely helpful in understanding what you've just read. After that MH gets into Kronecker products and Clebsch-Gordon coefficients as well as other operations with GR, and has another neat chapter afterwards on physical applications. He speak about the symmetric group in great length, and then about continuous groups, another extremely important chapter. The rest of the book uses the core of what you've just learned to help you understand linear groups in Hilbert space, and applications to sub-atomic physics.

Here's what you need to do to consume this book successfully:

1) Don't wait for MH to give you an example. Make them up as you go along! And make sure you fully understand each and every little statement he makes: there's no extravagant sentences here, all are vitally important and he will make use of every statement at least once to prove another point.

2) If you haven't had quantum mechanics yet, hold off on the last half of the book until you have! MH assumes this knowledge, but you can get away with your ignorance for the first part of the book, up until chapter six (and then you can skip around a little bit).

3) Know the fundamentals of group theory before you begin. It's true that MH doesn't assume this knowledge, but I assure it's vital for ease of reading. There are enough new concepts to absorb with out making your brain less permeable by not having group theory under your belt.

Overall, this book is good for physicists who want to become more adept in the language of theoretical physics (especially quantum mechanics and quantum field theory). I recommend it; but I also recommend you keep at least three other texts on hand that have their own way of explaining the things MH tries to explain. It is a good idea to do that in any independent learning venture, anyway.

This is one of those books that appear just before their subject matter becomes a fashion. The most famous example is Courant-Hilbert "Methods of Mathematical Physics", which contained the mathematics of quantum mechanics as if the authors had guessed what the future had in store. Hamermesh taught group theory for physicists just before SU(3), quarks, etc, dominated particle physics. Everybody learned groups from "Hamermesh". Now time passed, more specialized books appeared, physicists learned more mathematics... What of Hamermesh? Well, I always thought it was rather boring, a collection of methods with very little motivation. If one compares it with a modern book such as Inui, Tanabe, Onodera, one sees the difference: much more physical context. Hamermesh has, notwithstanding, done his job.

At the time I ran into this book I was doing research on martensitic transformations in metals. For that, as an engineer, I needed lots of information on point groups. The first chapter of the book contains the basics of group theory and teaches the totally ignorant all he has to know about the subject. The second chapter immediately deals with the point groups as one encounters them in crystallography. Very comprehensive and usefull information. Then the formal theory on groups is treated and general theorems are derived. For an average engineer without too much mathematical background this may be a bit too much, but the chapter is well written and provides usefull information that is used in chapter 4 to derive the irreducible representations and character tables for the point groups discussed in chapter 2. After that, I did not need the book anymore besides the short treatement of translation groups at the end of the book. I definately recommend te book for anyone who has to deal with point groups and wants to know more than just the basics.

My first impression is disappointment. While discussing permutation groups the author states that there are odd and even permutations essentialy leaving the proof to the reader. I think the proof that decomposition of a permutation into transpositions always has an odd or even number of factors (i.e. is unique) is not very trivial and I never encountered a math textbook which left the proof of this important statement to reader. If I had to derive importnt results by myself, breaking into the open door sometimes, I can do it without this book, I think.

It's a fine text, but Tinkham is probably the best route for the (particularly solid state) physicist.

A great book for a beginner. I recomend i