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Groups, Representations and Physics, by H.F Jones
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Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.
- Sales Rank: #1340234 in Books
- Brand: Brand: CRC Press
- Published on: 1998-01-01
- Released on: 1998-01-01
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .78" w x 6.14" l, 1.10 pounds
- Binding: Paperback
- 340 pages
- Used Book in Good Condition
Review
This work seems to cover virtually all the problems of physics for which group theory is helpful...strikes a good balance between mathematics and physical applications and should be valuable to researchers. It is well printed and produced and the paperback edition is good value.
Most helpful customer reviews
0 of 0 people found the following review helpful.
Rudiments With Applications
By G. A. Schoenagel
The author clearly states the readership as third year physics undergraduates.
Rigorous proofs of mathematical nature are eschewed.
Notation is uncluttered and a course in standard undergraduate quantum mechanics is assumed.
Given those constraints, this exposition of the interplay between groups and physics is a welcome addition to the available texts.
The first four chapters are rather elementary, presenting painless entree for the uninitiated.
We meet a nice discussion of induced transformations of the quantum-mechanical Wave-function in Chapter Three;
physical examples follow (Pages 38-43).
Comparison can be made between Young Tableaux, here (Pages 158-164) and Howard Georgi's text on Lie Groups.
The Middle chapters (5,6,7) cover various physics applications including ferromagnetism, molecular vibrations and
Clebsch-Gordan Coefficients.
The Hydrogen Atom and SO(4) explored (Pages 124-127) and Scattering theory concludes Chapter Seven.
The last three chapters (arguably) are the most satisfying aspect of this text:
applications to particle theory, Poincare and Gauge Groups.
It is well to remember "... there is a world of difference between ordinary and hyperbolic trigonometric functions" (Page 171),
this when discussing Special Relativity and the Lorentz Group in Chapter Nine;
the chapter concludes with a thorough derivation of "invariance of the helicity operator under rotations" (Page 191).
Appendix "E" presents recapitulation of Lagrangian Field Theory.
This book is not the place to turn for extensive mathematical rigor or technical considerations.
However, it does provide fascinating accounts of the relationship between group theory and modern physics
and should provide an interesting ingress for students of physics.
20 of 21 people found the following review helpful.
Covers a lot of ground, but not very well
By Client d'Amazon
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.
16 of 17 people found the following review helpful.
not good
By siyah corap
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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