This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.
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Book Description
Editorial Reviews
From Scientific American
"The book is clearly written and should be accessible to readers who have a good undergraduate preparation in mathematics or physics. Each part of the book ends with a list of references that will enable the reader to pursue the material presented in greater detail."
Review
"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." -- J Pullin, Classical & Quantum Gravity, 1995
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Most Helpful Customer Reviews
14 of 15 people found the following review helpful:
5.0 out of 5 stars
My favourite text of all time (so far),
By Mr. Sean (Toronto, Ontario Canada) - See all my reviews
This review is from: Gauge Fields, Knots and Gravity (World Scientific Series on Nonlinear Science) (Hardcover)
This book should be at the top of anyone's reading list who is planning to get into serious mathematical physics. It deals with a good deal of complex material, but the presentation is easy to follow, and shouldn't be beyond most advanced undergraduates. There are a lot of good exercises which fill in most of the gaps. (If you want a book heavy on detail, this book may not be for you. If you want a book that gives you all the tools you're going to need to get start understanding quantum gravity and other areas in a short time, get this book immediately!) It's a shame the paperback edition doesn't seem to be available anymore; it's half the price, and checking with the publisher reveals that the paperback edition is still in print.
14 of 16 people found the following review helpful:
5.0 out of 5 stars
Perfect,
By A Customer
This review is from: Gauge Fields, Knots, and Gravity (Series on Knots and Everything) (Paperback)
A beautifully written book which should be entitled "quantum gravity primer for the practical man". Clear and self-contained, this book will serve aa a small survey of mathematical physics, giving the reader tools in particle physics and gravity. Excellently motivated topics. Compact enough to bring with you anywhere. The only thing it fails at is dicing a proper tomato.
10 of 12 people found the following review helpful:
5.0 out of 5 stars
Worth its weight in gold!,
By A Customer
This review is from: Gauge Fields, Knots, and Gravity (Series on Knots and Everything) (Paperback)
I think the review above by J. Pullin puts it very well. This is a great book, and a good place to get started (it also provides suggestions for further reading). The authors have done a fantastic job, and I highly recommend the book!
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