Lie Groups for Pedestrians (Dover Books on Physics) by Harry J. Lipkin (PDF)

Description

According to the author of this concise, high-level study, physicists often shy away from group theory, perhaps because they are unsure which parts of the subject belong to the physicist and which belong to the mathematician. However, it is possible for physicists to understand and use many techniques which have a group theoretical basis without necessarily understanding all of group theory. This book is designed to familiarize physicists with those techniques. Specifically, the author aims to show how the well-known methods of angular momentum algebra can be extended to treat other Lie groups, with examples illustrating the application of the method.Chapters cover such topics as a simple example of isospin; the group SU3 and its application to elementary particles; the three-dimensional harmonic oscillator; algebras of operators which change the number of particles; permutations; bookkeeping and Young diagrams; and the groups SU4, SU6, and SU12, an introduction to groups of higher rank. Four appendices provide additional valuable data.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The author starts on page 2 of Chapter 1 “Introduction” in the book with a short summary of quantum mechanics of angular momentum and quantization operators for bosons. In order to appreciate the first few pages of this book, one needs to have worked through Chapters XIII and XXI of Volume II of Albert Messiah “Quantum Mechanics”. That can be obtained thru a graduate level education in Physics. After chapter 1, it proceeds into the mathematical details of developing Lie groups of importance for particle physics and quantum field theory. As a research physicist, this book added to my understanding of the importance of group theory in particle physics after working through 180 pages, and it was a lot of hard work. This book is good reference to graduate level courses in theoretical physics

⭐This book is a nice, concise review of Lie algebras and groups as they are used in particle physics. The content is a bit dated, but the explanations of building the mathematical operators used in quantum mechanics are quite lucid. I think this would be an excellent companion to a more modern text on particle physics. This book is NOT Lie groups 101. Topics include the different flavors of spin, harmonic oscillators, multiplets of a few SU(n) groups, and tying everything back to Young diagrams.The title is a bit misleading- if this is the “pedestrian” approach, I would hate to see what the author thinks is the more exotic route. The book jumps in right at basic angular momentum operators, so if it’s been a while you might need to break out notes from a QM class. Important concepts are not defined, or are left as a vague mathematical mumbo-jumbo that doesn’t at all hint at the underlying physical concept. Many times the author says “it clearly follows that…” or something similar, but I found it a nontrivial exercise to follow. Despite the fact that I had to go to other sources and push my pencil around a bit (probably my own shortcomings than anything in the book), I found this book easy enough to learn from.

⭐This is the best book I have come across to explain Lie groups/algebras to someone who has at least taken an introductory quantum mechanics course and is comfortable with the angular momentum operators-more particularly the raising/creation and lowering/annihilation operators. This is not for someone who has watched NOVA and wants to learn more. If you have a good background in group theory and quantum mechanics, or even a very basic understanding of them and you want to learn more about the fascinating word of Lie Algebras/groups, this book is for you.As a companion to this book I would highly recommend Lie Groups, Lie Algebras, and Some of Their Applications by Robert Gilmore. This book gives an excellent exposition of the subject, going into more detail than Lie Groups for Pedestrians, but not so much detail that you need to have taken a course on group theory in order to digest the information. It also has very informative exercises at the end of the chapter, which in my opinion is a plus.If you’re looking for a quick and dirty introduction to string theory and that ilk, this is not your ticket. If you are looking to expand your horizons of QM theory and second quantization-which leads to wonderful results and ‘toys’ in not only particle physics, but also in spectroscopy of atoms and molecules-this is your book.

⭐I like the fact that it is compact and avoids a lot of the abstractions that might only be used by mathematicians.It is a different way of approaching the subject but difficult to relate to other approaches, if your expertise in adding quantum angular momentum is limited like mine, but I am still working on the book, part way thru at this time, to see if it broadens my intuitive grasp of the subject. Hard to say what others should know before buying it until they read it and see if it applies to their needs. Check out the Sakaton model on the sample pages and see if you can relate to it. I’ve never seen anything quite like this book, but apparantly it is based on the published work of a number of researchers.

⭐Good book to start learning lie groups

⭐This book, by physicist Harry Lipkin, was intended as a quick introduction to Lie Groups to other physicists like himself working in the mid 1960’s. At that time, many physicists had a sophisticated mathematical skill-set, but not one that included Lie Groups and Algebras, nor understood to the degree it is understood today how much it helps to think along those lines. Dr. Lipkin wanted to spread the knowledge of Lie Groups to physicists would would benefit from it.As such, a “pedestrian” would be expected to be familiar with the then-current formulations of quantum theory, including the matrix and operator representations of quantum mechanics, as well as all the calculus necessary to work those theories. This is evident in chapter 1, where on page 2 section 1.1 is titled “Review of Angular Momentum Algebra”, and whose first sentence asks us to consider the operators Jx, Jy, and Jz, which have the “well known” commutation rules [Jx,Jy]=iJz (etc).Pedagogically, this is sound: start with something you know the reader is familiar with, then show by analogy how that applies to the new topic you are introducing, then expand the techniques into new areas, and then presumably turn it back towards the topic the reader knows and show how Lie Groups (in this case) make things easier.However, it requires knowing the audience — or, conversely, being the intended audience. I am not; from the benefit of knowing where physics has gone in the intervening 42 years, I know Lie Groups are important, and I know that my understanding of physics is weak, and I was hoping knowing about Lie Groups would help my understanding of physics. Ultimately, this book lost me before page 5.I suspect this book no longer has an audience. The importance of Lie Groups in physics is now well-recognized and is taught to physicists-in-training. The folks who would understand this book no longer need it. Historically, it might have been important, but it no longer is.

⭐By “pedestrian”, Dr Lipkin apparently means anyone with a sound knowledge of physics at the graduate level, with some expertise in quantum theory. If you have all that, the book is a breeze, explaining why group theory has become such an important part of modern physics. Note, however, that this is a Dover reprint and that the book was originally published in 1966. Much has happened to physics during the last half-century and you should look for something more recent if you really need to know what’s going on.

⭐A good and light “walking tour” of Lie Groups and their fundamental usefulness. Easily accessible to most who have understood algebra even a little.

⭐Formación muy básica que no incluye los grupos continuos que es lo que yo buscaba. De todos modos es una buena lectura con aplicaciones físicas.

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⭐～本書があるのは知っていたが、学生時代には実物を見ることがなかった。今回Dover版が出ているのを知り、懐かしさにひかれて購入した。書名からは非専門家向けの解説書と思えるが、実際は量子物理と素粒子物理学者のための群論の入門書だ。導入にアイソスピンを持ってきて、SU(3)、生成消滅演算子、ヤング図形の解説が丁寧になされている。これら基礎にして、ハド～～ロンの対称性と分類を扱っている。原著の出版が1966年なので、クォーク模型よりも坂田模型（Sakaton）の解説が多い。固体物理学者向けの話題はないし、ローレンツ群などの解説はなく、今となっていは、扱っている話題が狭いと感じる。そのため、当時の話題を知りたい人には面白いだろうが、多くの人に積極的に進める理由はない。～

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