Customer Reviews

Lie Groups, Lie Algebras, and Some of Their Applications (Dover Books on Mathematics)

5 star:		(8)
4 star:		(0)
3 star:		(0)
2 star:		(1)
1 star:		(0)

 

 

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".

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.

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.

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.

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!

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 find Professor Gilmore's book a top-flight exposition of a "not so easy" subject. As a mathematician, I am very comfortable with the degree of mathematical rigor. It is not sloppy. I hope physicists won't be put off by the fact that this book is written in "mathematics." We are in a time when the distinction between pure mathematics and theoretical physics is rapidly blurring, if not already extinct. The physicist must become accustomed to the protocal of pure mathematics, as the mathematician must understand the needs of theoretical physics and be motivated by them. Many will disagree.

As a Ph.D candidate in mathematics a "few" years ago, on creating a proof (hopefully elegant), I used to joke with my major professor about what a disaster it would be if the physicists at our university found some way to put our reselt to practical use.
Imagine the horror of our lemma on ideal theory in a C* Algebra
being so desecrated. Oh, the shame! Now I say "a pox on such elitism and snobbery."

The work under discussion is very well motivated (the preface is an excellent historical summary of how this mathematics became so necessary for progress in physics, and how theoretical physics has motivated mathematical research. The copious "no frills" illustrations are particularly valuable to the reader, particularly if she is not accustomed to just accepting chains of head-to-tail syllogisms as sufficient.

Two thumbs up!

I'm really enjoying this text - several of my math books, as much as I love them, are so dense that at times I feel like I'm slogging through them. What I really appreciate about this book are the excellent figures and comprehensive summary tables; these are thoughtfully made and help solidify concepts and/or "big picture" ideas. I generally avoid books with too many words (I find that my style of learning leans towards equations, pictures, worked examples, and efficiently stated insights), and this text strikes just the right balance.

Couldn't get into this, I gave up in the first chapter after failing to understand how he was applying his Kronecker product to his vectors. He just failed to explain his notation adequately. *And* there were mistakes in that first bit I read up to then.

I appreciate that physicists and mathematicians use different language, and I also appreciate that this was an advanced work, i.e. postgrad plus, but it would have been nice to have seen a glossary of terms and a little more background.

This may be a competent and erudite work, but unfortunately impenetrable without unspecified previous knowledge, and that's not the way these books ought to be.