- Series: Dover Books on Mathematics
- Paperback: 464 pages
- Publisher: Dover Publications (June 1, 1950)
- Language: English
- ISBN-10: 0486602699
- ISBN-13: 978-0486602691
- Product Dimensions: 5.4 x 0.9 x 8.5 inches
- Shipping Weight: 1.1 pounds (View shipping rates and policies)
- Average Customer Review: 9 customer reviews
- Amazon Best Sellers Rank: #1,340,485 in Books (See Top 100 in Books)
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The Theory of Groups and Quantum Mechanics (Dover Books on Mathematics)
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About the Author
Hermann Weyl: The Search for Beautiful Truths
One of the most influential mathematicians of the twentieth century, Hermann Weyl (1885–1955) was associated with three major institutions during his working years: the ETH Zurich (Swiss Federal Institute of Technology), the University of Gottingen, and the Institute for Advanced Study in Princeton. In the last decade of Weyl's life (he died in Princeton in 1955), Dover reprinted two of his major works, The Theory of Groups and Quantum Mechanics and Space, Time, Matter. Two others, The Continuum and The Concept of a Riemann Surface were added to the Dover list in recent years.
In the Author's Own Words:
"My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."
"We are not very pleased when we are forced to accept mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context."
"A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details." — Hermann Weyl
Critical Acclaim for Space, Time, Matter:
"A classic of physics . . . the first systematic presentation of Einstein's theory of relativity." — British Journal for Philosophy and Science
Top customer reviews
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 He employs outdated and non-standard terminology and notation, and while his discussion of representation theory and applications in physics are certainly lucid some of the most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.
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.
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.
One may legitimately give 5 stars to any of Hermann Weyl books-- as he was not only a grand mathematician but also a prominent philosopher and physicist who with his open-mindedness and creativity contributed much to each faculty in the 20th century. However one may wonder why his books written long ago cannot be offered by Amazon as free e-books (in Kindle edition). Of course if you are a researcher, the Kindle edition lacks the page number you need in your reference. In any case, there is no such a short-come in the FREE PDF versions of Weyl books that you can easily find on internet and download, they include:
__Space, Time, Matter
__Philosophy of Mathematics
__Mind and Nature
__The Theory of Groups and Quantum Mechanics