Lie Groups, Lie Algebras, and Some of Their Applications

An excellent overview of Lie Groups and Algebras. Gilmore, as he notes himself, has concentrated on producing a self contained course for physicists. The mathematical treatment is generally detailed and shows most steps. He notes the omission of various topics in physics and mathematics, but refers the reader to specialized texts in his comprehensive bibliography. My course of Lie Groups at university was focused on mathematical applications and differential equations and this text by Gilmore provides a satisfying broader appreciation of Lie Groups and Algebras in their own right and their applications to fields and problems I wasn't previously aware of. I'm especially pleased with the many exercises which I find a great help in developing greater understanding and testing my grasp of the text.

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.

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".

Gilmore's treatment of Lie groups and Lie algebras is written in the mathematical languague 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 and cheap!

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.