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Title: Geometry, Topology and Physics (Graduate Student Series in Physics) by Mikio Nakahara ISBN: 0-7503-0606-8 Publisher: Institute of Physics Publishing Pub. Date: 01 October, 2003 Format: Paperback Volumes: 1 List Price(USD): $55.00 |
Average Customer Rating: 4.29 (7 reviews)
Rating: 4
Summary: Flat spheres and more
Comment: Highly stimulating and extremely hard to read, written for mathematicians in physics. However, the chapter on Riemannian Geometry can be worked through, up to a point, without any knowledge of exterior differential forms, and is notable if for only one fact alone: a simple calculation is provided that explains explicitly that spheres in four and eight dimensions (3-spheres and 7-spheres) are flat with torsion! I don't know another reference that a physicist without special background in math can consult to understand this highly nonintuitive fact.
Rating: 2
Summary: Just a "better than nothing" book
Comment: It's not the best way to learn geometry / topology for physics. It's better than nothing, though, if you are familiar with the topics already. There are many "holes" in Nakahara's book, which you would spend much more time and hard working in a "big" library. than you should to fill in. It's not worth that money and struggle. It's the last one you should consider about owning.
If you are a physics graduate who needs a nice guide to "understand" the aspects and skills of geo / top, I would recommend the following: (1) Milnor's Topology from the Differentiable Viewpoint, and (2) Kreysig's Differential Geometry. The first one was old, and so it does not assume much knowledge about the topic. The latter is a kind-of-Bible for the topic, and all solutions are provided for the problems. These two books will help you a lot if you care about the meaning, not only for those classroom exams or just showing off that you know something about it. Frankel is the next to put on your bookshelf as a detailed and rigorous development for your preparation to be a theoretical physicist.
If you have only a rough idea about topology, Hocking and Steen are the best choices, and they are Dover!!
Anyway, if I could find a cheap used Nakahara, I would get it as a reference.
Rating: 5
Summary: Best in its genre
Comment: I suppose I should preface this by saying that I read this book *after* reading similar books, so my ability to understand this book is probably better than others, but that said, I think that my comparative evaluation is free from this bias...
There seem to be a few books on the market that are very similar to this one: Nash & Sen, Frankel, etc. This one is at the top of its class, in my opinion, for a couple reasons:
(1) It's written like a math text that covers physics-related material, not a book about mathematics for physicists. I prefer this; you may not. As a consequence, this book is more rigorous than its alternatives, it relies less on physical examples, and it cuts out a lot of lengthy explanation that you may not need. Of course, there are drawbacks to all of these "features" -- you need to decide what you need and what's best for you.
(2) It's most comprehensive, with Frankel coming in second, and Nash & Sen least comprehensive (though they have quite a bit on Fibre bundles and related topics). Nakahara has a chapter on complex manifolds, which is absent from the other two. Nakahara also concludes with a nice intro to string theory, which is absent from the other two as well (though nothing you couldn't find in Polchinski or the like). Actually -- I modify this slightly. Frankel covers less subjects than Nakahara, but with more depth (though also more wordiness -- I quit Frankel about 2/3 through because it wasn't succinct enough and I got tired of it).
Depending on your tastes, I would recommend this book before the other two.
It presupposes that you have an understanding of algebra (groups, rings, fields, etc.) but it has an introduction to the necessary components of topology within. Frankel has presupposes both algebra and topology; Nash & Sen presupposes only algebra.
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Title: Supersymmetry and Supergravity by Julius Wess, Jonathan Bagger ISBN: 0691025304 Publisher: Princeton University Press Pub. Date: 03 March, 1992 List Price(USD): $47.50 |
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Title: Geometrical Methods of Mathematical Physics by Bernard F. Schutz ISBN: 0521298873 Publisher: Cambridge University Press Pub. Date: 01 December, 1980 List Price(USD): $36.95 |
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Title: D-Branes by Clifford Johnson ISBN: 0521809126 Publisher: Cambridge University Press Pub. Date: January, 2003 List Price(USD): $65.00 |
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Title: Spacetime and Geometry: An Introduction to General Relativity by Sean Carroll ISBN: 0805387323 Publisher: Pearson Addison Wesley Pub. Date: 20 June, 2003 List Price(USD): $83.00 |
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