The Theory of Groups and Quantum Mechanics (Dover Books on Mathematics)

This is my favorite introduction to quantum mechanics. It is a difficult book, because it is succinct, though clear, and reflects Weyl's powerful intellect and original approach at every step. Each page is a challenge, but worth the effort.

Weyl was ahead of his time by a good 40 years. Following a general introduction to quantum mechanics and group theory Weyl explores the ideas of applying symmetry groups and algebra to problems of quantum mechanics.Unfortunately for today's reader, especially one who has been thoroughly exposed to quantum mechanics and group theory in a rigorous setting, Weyl's book is dated in its material and especially in its notation and presentation. He employs outdated and non-standard terminology and notation, and while his discussion of representation theory and applications in physics are certainly lucid some of the most brilliant applications of group theory (gauge groups, and applications in the standard model) are entirely missing - having been discovered roughly 40 years later. There are better textbooks on linear algebra, quantum mechanics, group theory, representation theory, and applications of group theory to QM (roughly the divisions of this text) and at the very least modern texts will not be burdened with the artificial barrier caused of antiquated terminology and notation. In short, this is not a book to start learning the subject, but is certainly interesting in its own right as a historic text.

My copy of this book dates back to a Dover edition from 1960 when it cost $1.95. It is still a bargain.The extremely clear and closely argued discussion in this book is unparalleled in any other text. It exemplifies an intuition and a rigor that is astounding to experience, and raises one's estimation of the capacity of man and abstract thought.It is also an extremely practical and educational experience in mathematical technique, and how it can illuminate physical theory and experiment, not just mathematics.As an alternative view, CN Yang has said about this book that "Almost every theoretical physicist born before 1935 has a copy...but very few read it. Most are not accustomed to Weyl's concentration on the structural aspects of physics and feel uncomfortable with his emphasis on concepts. The book was just too abstract for most physicists."I regard that remark as illuminating the mindset of some physicists. Draw your own conclusions.

Written in the early years of the quantum theory, the author of this book foresaw the importance of considering symmetry in physics, the use of which now pervades most of theoretical high energy physics. Indeed, with the advent of gauge theories, and their experimental validation, it is readily apparent that symmetry principles are here to stay, and are just not accidental curiosities. A reader of the book can still gain a lot from the perusal of this book, in spite of its date of publication and its somewhat antiquated notation. Older books also have the advantage of discussing the material more in-depth, and do not hesitate to use hand-waving geometrical pictures when appropriate. This approach results in greater insight into the subject, and when coupled with eventual mathematical rigor gives it a solid foundation. One example where the discussion is superior to modern texts is in the author's discussion of group characters and their application to irreducible representations and spectra in atomic systems. The reader will no doubt probably want to couple the reading of this book with a more modern text so as to alleviate the notational oddities in this book. The author's presentation is clear enough though to make an appropriate translation to modern notation. The reader will then be well prepared to tackle more advanced material in mathematical and theoretical physics that make use of the group-theoretic constructions that take place in this book.

The other one is Wigner's "Group Theory and Quantum Mechanics". As it is true of the other great books by Weyl, this is not an easy book, but it is, by all means, accessible. Don't try to read it in front of the TV set. Get pencil and paper, put yourself in a calm and contemplative mood and patiently read the words of the master. Hermann Weyl, one of the great minds of the 20th century, wrote this book with utmost care to make it self-contained. Sometimes you have to be deep in order to be brief, so the book requires some thought. But the main ideas are all there, and the connection of group theory with quantum mechanics has here its best treatment, in my humble opinion. But in less humble too: this was the only book concerning physics which Enrico Fermi read as a grown up. Once, Max Born had to write a synthetic exposition of Quantum Mechanics. After he finished it, he saw, for the first time, this book, and Weyl's synthesis of QM. He felt depressed by the superiority of Weyl's text. The book was originally written in German, but the translation is excellent, due to the great American cosmologist H. P. Robertson, of Robertson-Walker fame.

Herman Weil's masterpiece now available at an affordable priceWhat is not to like

Clarté, rigueur, complet et surtout très utile pour la compréhension des différentes théories des ensembles et pour leurs applications à la physique.Nécessite la connaissance de l'anglais et des maths supérieures modernes et de posséder une bonne base en physique théorique et des notions solides de mécanique quantique.

ワイルの名著誉れ高い本、原文は独逸語で、その英訳ではあるが興味持って読んでいます。Dover 出版には手に入りやすい価格で古いが今でも教育的な理数系の名著が多数ありますね。日本にはこのような出版社がないのが残念です。英語に苦が無ければ若い人にも手が出せる価格なのでどんどんチャレンジしてもらうことを希望してます。