- Paperback: 480 pages
- Publisher: World Scientific Publishing Company; 4 edition (1 January 1994)
- Language: English
- ISBN-10: 9810220340
- ISBN-13: 978-9810220341
- Product Dimensions: 15.2 x 2.5 x 22.9 cm
- Average Customer Review: 1 customer review
- Amazon Bestsellers Rank: #42,755 in Books (See Top 100 in Books)
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Gauge Fields, Knots and Gravity: 4 (Series on Knots & Everything) Paperback – 1 Jan 1994
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"This book is a great introduction to many of the modern ideas of mathematical physics including differential geometry, group theory, knot theory and topology. It uses as 'physical excuses' to introduce these topics Maxwell theory, Yang-Mills theories and general relativity (including its Ashtekar reformulation). The level of the book is gauged to advanced physics/math undergraduates and graduate students. The style of the book is quite lively and explanations are very clear. The treatment is mathematically and physically self-contained ... I would strongly recommend this nicely written book for anyone interested in teaching the contemporary ideas of mathematical physics to an audience of physicists (especially if that audience is interested in particle physics/gravity). It offers an excellent way of treating the subject with mathematical rigor while keeping the physical motivation and usefulness of these mathematical concepts close at hand. For the individual reader, it is a great way to be lured into the study of the mathematics that underlies contemporary theoretical physics."
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Most helpful customer reviews on Amazon.com
The author abuses notation quite uncomfortably. As a physicist trying to learn math, at times the author mixes the mathematicians need for rigor with the physicists sloppy shorthand. And it leaves me utterly baffled. When we are defining the standard flat connection on sections as smooth whatevers over a local trivialization, I find that leaving the fact that we pulled back two things and pushed forward two others to be confusing. I tend to get lost trying to break down the steps. I'll look at a definition and break it down piecewise and associate different facts about the object to other definitions. And then I'll think I screwed up because something is missing, but in reality this being pushed forward was "trivial."
Had quite a few occurrences where I try to understand everything from a mathematicians point of view and get lost only to realize that he was just being sloppy like a physicist would. I think a little more consistency would have been great. If he is going to belabor pull backs in one section and then ignore then in the next, it needs to be clearly stated.
Also, every single notation used involved parenthesis. A(v) = v(A,v(a))= (Ava(A())V). Really, there are a dozen different delimiters that we could have used. Why does everything have to be enclosed in parenthesis?
Aside from these two nitpicks, the book up there with the best I've ever used.
It's a delight to read this book. Even by reading the introductions to all the chapters an 'uninitiated' explorer can actually get a good idea of how these exotic areas of mathematics are interconnected and can be used to describe physical realities. There is a great deal of aestehtics in this interplay, and the book brings them out in its true spirit.
The authors are rigorous, but definitely not so much as some of the standard texts in these areas. And they admitted it in the preface itself. The book is like an 'invitation' to this extraordinarily beautiful and modern area of mathematical physics.
I am a great fan of John Baez. He has been writing an excelling series of blogs (TWF, and then Azimuth) for a long time, and that IMO probably ranks into the class of the finest ever science writings. No wonder the book carries the strain of the same genius, that of explaining the abstruest in simplied manner, in abundance.
It should give quite a lot of material to digest for mastery of the subject.