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Topology and Geometry for Physicists Paperback – February 11, 1988

3.9 out of 5 stars 14 customer reviews

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Editorial Reviews

Review

"One of the most remarkable developments of the last decade in the penetration of topological concepts into theoretical physics. Homotopy groups and fibre bundles have become everyday working tools. Most of the textbooks on these subjects were written with pure mathematicians in mind, however, and are unnecessarily opaque to people with a less rigorous background. This concise introduction will make the subject much more accessible. With plenty of simple examples, it strikes just the right balance between unnecessary mathematical pedantry and arm-waving woolliness...it can be thoroughly recommended.
--T.W.B. Kibble, PHYSICS BULLETIN

From the Back Cover

This volume provides an easily comprehensible introduction to topological and geometrical methods in theoretical physics and applied mathematics. No detailed knowledge of topology or geometry is required in the reader, and advanced undergraduate or graduate physicists should have no difficulty in understanding the material.
The style and approach of the book reflect the fact that the authors are themselves physicists, and have taken trouble to clarify difficult mathematical concepts and to emphasize their physical motivation. The applications range from condensed matter physics and statistical mechanics to elementary particle theory, while the main mathematical topics are differential forms, homotopy, homology, cohomology, fibre bundles, connection and covariant derivatives and Morse theory.
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Product Details

  • Paperback: 311 pages
  • Publisher: Academic Press (February 11, 1988)
  • Language: English
  • ISBN-10: 0125140819
  • ISBN-13: 978-0125140812
  • Product Dimensions: 9 x 6 x 0.7 inches
  • Shipping Weight: 13.6 ounces
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #5,789,746 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Paperback
Nash's book commits the sin many mathematical physics textbooks out there commit: "oh, we're writing for dimwit physicists, lets just give them a few scrawny examples and assure them everything else works alright." I'm sorry but writing for physicists is NOT an excuse for writing a sloppy textbook. Would you feel alright not knowing how an integral is defined? Would you use a numerical evaluation software to calculate integrals in serious research without understanding the algorithm it uses? If you do then you're a pretty shoddy physicist. I'm not saying this out of some "macho" sentiment many purist physicists have - I'm simply saying this because I feel the way this book teaches you diff. geometry is wrong - it teaches you to draw pictures and go by the pictures. When the pictures run out, so does your understanding.

This book is supposed to teach differential geometry. However, very little can be learned from it unless one already knows differential geometry: definitions are sometimes not general and sometimes not present at all, theorems are often stated only for special cases and even more often than that not proved at all. Sure, the book offers nice geometrical intuition, but this is not enough. An example: the book "proves" Stoke's theorem around page 40. Now, even a rigorous and condensed book would have problems doing that, considering the amount of "machinery" one needs to build up for it (tensors, differential forms, manifolds and so forth). This means the book makes a mess of it - big time.
There are many fine diff. geometry books out there, some for physicists, some not, which you should check out - Nakahara's text is so much better. For geometrical intuition I suggest picking up Schutz's book.
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Format: Paperback
When reading this book one can both admire these authors and feel sympathy with them. They have made an honest effort to explain the concepts of differential geometry and topology in a way that is understandable and appreciated by the physicist reader. But the book falls short in many places, although there are some places where they do a fine job. They have taken on a very difficult project in this book, for it is quite straightforward to expound on the formalism of mathematics, but explaining it in a way that grants insight into its conceptual meaning is another matter altogether. Many physicists complain, with justification, that the way mathematics is presented in textbooks is not sufficient for giving them a deep appreciation of the underlying ideas involved. This, they argue, is what is needed for devising new physical theories and results based on these ideas. Physicists must assimilate very complex mathematical ideas very quickly in order to formulate these theories in a reasonable time frame. This is especially true in high energy physics, which in the last two decades has used mathematics like it has never been used before. Indeed, the mathematical complexity of high energy physics is dizzying, and if progress is going to be made in this field by the students of the 21st century, they are going to need mathematics books and documents that are more than just formal expositions. But, again, writing these kinds of books is very hard to do, and has yet to be done in a book to this date, although there are helpful discussions scattered throughout the mathematical literature.
Some of the concepts that need more in-depth explanation include: the theory of characteristic classes, sheaf theory, the theory of schemes in algebraic geometry, and spectral sequences in algebraic topology.
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Format: Paperback Verified Purchase
I must say that this wonderful little book must be (and I recommend it as such) the first step for a physicist into the world of higher geometry (manifolds, differential forms, stokes theorem, curvature, etc), differential and algebraic topology where topics like Homotopy, Homology, Cohomology theories, the theory of Fiber bundles, characteristic classes and Morse theory appear. The authors are brilliant expositors and know their subject well, they oftenly give handiful insights into the subjects being treated and write so beautiful it makes think you are reading a Tolkien's story!. I believe this book should be a classic, for example I found it cited on another good book about group theory for particle physics (Costa and Fogli, Symmetries and Group Theory in Particle Physics), it is also cited in Nakahara. The book ends with some more physics like Yang-Mills theories from a geometric perspective where concepts like instatons and monopoles are treated. After this title you will be in a better position to address more terse books like Nakahara which at times requires a bit more of mathematical maturity. If I have to resume I would say it has been beautifully and clearly written, all in all, simply brilliant!!
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Format: Kindle Edition
Rigorous is not an absolute category: something is rigorous or it is not ; it is a relative one: something is more or less rigorous than something else.
When an author writes a book on mathematical methods for physicists, he may intend to convey to his audience a sound intuition about the subject ; something similar happens to Advanced Calculus, that is not the same as Introduction to Analysis.
If you can understand what is going on helped by pictures, even intuitively, kudos! You already know a lot. Sophisticated mathematics is not a substitute for lack of physical insight.
During decades methematicians mocked physicists because of delta Dirac function; now, distribuitions are a perfectly respectable branch of pure mathematics.
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