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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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Lie group theory plays an increasingly important role in modern physical theories. Many of its calculations remain fundamentally unchanged from one field of physics to another, altering only in terms of symbols and the language. Using the theory of Lie groups as a unifying vehicle, concepts and results from several fields of physics can be expressed in an extremely economical way. With rigor and clarity, this text introduces upper-level undergraduate students to Lie group theory and its physical applications.
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.


  • 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: 21.5 x 13.9 x 3 cm
  • おすすめ度: 5つ星のうち 5.0  レビューをすべて見る (1 件のカスタマーレビュー)
  • Amazon 売れ筋ランキング: 洋書 - 57,532位 (洋書の売れ筋ランキングを見る)
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5つ星のうち 5.0


3 人中、3人の方が、「このレビューが参考になった」と投票しています。 投稿者 FANTASMA UCCIDENDO MECCANISMO (YO SOY AQUEL) トップ500レビュアー 投稿日 2008/11/27
形式: ペーパーバック
Gilmore's treatment of Lie groups and Lie algebras is written in the mathematical language which theoretical physicists should be comfortable with. The notation is very clear, the discussion is nearly flawless and the physical relevance is not omitted, which is for example done in more mathematically oriented books. Very thorough, very readable. Perhaps the best feature of this book is that it aims to convey the theory of Lie algebras and Lie groups to physicists. In doing so, the author is careful to give a very simplistic approach so that one not familiar with the subject can understand it. ...続きを読む ›
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不正使用の報告 で最も参考になったカスタマーレビュー (beta) 12 件のカスタマーレビュー
43 人中、40人の方が、「このレビューが参考になった」と投票しています。
Rave Review 2006/11/10
投稿者 Michael Cloud - (
形式: ペーパーバック Amazonで購入
I haven't read this whole book cover to cover, because of time constraints. However, I can say that it is extremely clear in it's exposition. The material is very well chosen for use by physicists. I have read pure math books on this topic, and while they can be more sophisticated and thorough, they are rarely as straight forward, nor do they cover the breadth of material in this book.

In sum I would have to agree with what I was told: "this is the book on Lie Algebra for a physicist".
51 人中、46人の方が、「このレビューが参考になった」と投票しています。
Excellent introduction to the field for physicists 2000/1/23
投稿者 A.X. Razza - (
形式: ハードカバー
Perhaps the best feature of this book is that it aims to convey the theory of Lie algebras and Lie groups to physicists. In doing so, the author is careful to give a very simplistic approach so that one not familiar with the subject can understand it. Not to say that the book is elementary, since it builds rapidly into the far more interesting aspects of Lie Groups. A very good read.
42 人中、37人の方が、「このレビューが参考になった」と投票しています。
This book becomes my reference on group theory in physics 2006/12/30
投稿者 Roger Bagula - (
形式: ペーパーバック
I've waited many years to find a book like this.

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.
18 人中、17人の方が、「このレビューが参考になった」と投票しています。
Lie groups, not just for particle physics 2008/12/6
投稿者 J. A. Hansen - (
形式: ペーパーバック
Having read, and loved, Lie Groups for Pedestrians, I picked up this book to further my knowledge of this wonderful subject.
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.
12 人中、12人の方が、「このレビューが参考になった」と投票しています。
Too ambitious and unfriendly -- look elsewhere 2013/4/14
投稿者 J. R. G. Mendonca - (
形式: ペーパーバック Amazonで購入
Simply put, I didn't like the book. It is too ambitious and this is bad for the reader, that can easily get lost amidst too many irrelevant details.

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."
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