- ペーパーバック: 608ページ
- 出版社: Dover Publications (2006/1/4)
- 言語: 英語
- ISBN-10: 0486445291
- ISBN-13: 978-0486445298
- 発売日： 2006/1/4
- 商品パッケージの寸法: 13.9 x 3 x 21.5 cm
- おすすめ度： 1 件のカスタマーレビュー
- Amazon 売れ筋ランキング: 洋書 - 6,140位 (洋書の売れ筋ランキングを見る)
Lie Groups, Lie Algebras, and Some of Their Applications (Dover Books on Mathematics) (英語) ペーパーバック – 2006/1/4
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An opening discussion of introductory concepts leads to explorations of the classical groups, continuous groups and Lie groups, and Lie groups and Lie algebras. Some simple but illuminating examples are followed by examinations of classical algebras, Lie algebras and root spaces, root spaces and Dynkin diagrams, real forms, and contractions and expansions. Reinforced by numerous exercises, solved problems, and figures, the text concludes with a bibliography and indexes.
Robert Gilmore is a Professor in the Department of Physics at Drexel University, Philadelphia. He is a Fellow of the American Physical Society, and a Member of the Standing Committee for the International Colloquium on Group Theoretical Methods in Physics. His research areas include group theory, catastrophe theory, atomic and nuclear physics, singularity theory, and chaos.
Amazon.com で最も参考になったカスタマーレビュー (beta)
In sum I would have to agree with what I was told: "this is the book on Lie Algebra for a physicist".
It may take me many years to master everything in it,
but at least with this book I have a chance to try.
I contrast this text to books and papers by Gell-Mann, Richard Feynman,
and Steven Weinberg and these great men come off second best
when it comes to exposition of the relationships between groups.
I have found what appear to be factor of two difference
between the examples and the tables for A(n)
but those once corrected seem to leave this the complete
reference on group theory for physics that I've been looking for for a long time.
I congratulate Robert Gilmore for his well written book.
I am not a particle physicist nor am I mathematician, I am a spectroscopist and had read some about Lie groups and their applications to spectroscopy. However to read and digest the material that was contained in the books and articles I was coming across, it was clear that I needed to know more about Lie groups and algebras. This book was exactly what I needed. It gave very clear and concise definitions (if you have had an introduction to group theory) of what Lie groups and algebras are and the tools that are needed to use them.
The exercises at the end of the sections were a real joy for me. Working problems is the best way to learn a subject like this, and they helped to clarify what the preceding chapter had talked about. The writing is anything but dry and an easy read.
To start this book I would recommend that if you are a scientist you have taken, and understood, a good introductory course to QM and group theory; if you are a mathematician that you have taken and understood a good abstract algebra course. Do not do yourself a disservice by trying to digest this book without the proper background. You will most likely turn yourself off from a very beautiful and exciting area.
This book is not for someone who has taken an intro to physics course and wants to know about all the riddles of the universe. They will be lost, frustrated and otherwise flummoxed by this book.
The author himself states in the preface of his newer book (R. Gilmore, "Lie Groups, Physics, and Geometry") that "Over the course of the years I realized that more than 90% of the most useful material in that book [the one being revised here] could be presented in less than 10% of the space." What else can I say?
The application-minded readers (e.g., physicists) will suffer from its style and contents, and the mathematician can find much better presentations elsewhere in the vast literature on the subject. So... who needs it? I enjoyed and profited much more from the book by B. G. Wybourne, "Classical Groups for Physicists."