Analysis, Manifolds and Physics. Revised Edition | 
 enlarge | Authors: Yvonne Choquet-bruhat, Cecile Dewitt-morette
Publisher: North Holland
Category: Book
List Price: $85.95
Buy New: $68.76
You Save: $17.19 (20%)
New (9) Used (2) from $52.00
Rating:  5 reviews
Sales Rank: 894310
Media: Hardcover
Edition: 7th repr. 1996
Pages: 650
Number Of Items: 1
Shipping Weight (lbs): 2.9
Dimensions (in): 9.5 x 6.7 x 1.3
ISBN: 0444860177
Dewey Decimal Number: 515
EAN: 9780444860170
Publication Date: January 1, 1982
Availability: Usually ships in 24 hours
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Product Description
This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.
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| Customer Reviews:
an inspiration March 9, 2002
Alex (MTL)
12 out of 13 found this review helpful
This is the book that inspired me as an undergraduate to learn and appreciate, to a large extent, how physics and mathematics cohabit so beautifully. I continue to see, to this day, as a graduate student, how many of the recent developments in theoretical physics have been inspired by new mathematics and conversely. I still refer to this book on occasion, since it is laid out in a style that is amenable to mathematicians (such as myself!). It's an excellent read, and I highly recommend it (even as bed time reading!) Best regards, A.
A treasure for physicists August 25, 1998
henrique fleming (Sao Paulo, SP Brazil)
14 out of 16 found this review helpful
I use this book constantly. At first I thought it was good only as a reference, but now I know it is possible to actually LEARN any of its subjects from scratch. I particularly like its chapters on manifolds, Lie Groups and bundles. Connections on a principal bundle is extremely well done, with a translation to physics (gauge theories) performed in detail in an exercise (so to speak). Some time ago David Ruelle said that the physicists needed a presentation of recent mathematics in the form of Bourbaki's "Fascicule des resultats", a synthesis of the subject with complete definitions, examples and theorems clearly stated, but with the proofs ommited. This is it, except that in this book most demonstrations are not ommited, only those too complicated. The whole book is extremely readable, if you concentrate, turn out the TV, etc. A precious book.
A must have desk reference and educational tool September 28, 1999
10 out of 11 found this review helpful
This was the most reliable (and compact) source of mathematical information that I could find. I used it (almost exclusively) to teach myself what I needed to know to do my PhD thesis in General Relativity with Torsion fields. It is very overwhelming to look at the book the first time. But give it time. It is well written and inviting. The only draw back for me was the very small print.
Simply the Best in its League May 23, 2007
akrech
5 out of 5 found this review helpful
I have been looking for a book like "Analysis, Manifolds and Physics: Part I" for a long time. It combines all the features I think a book for physicist interested in mathematics (or vice versa) should have. It is very clearly written, it gives precise definitions, it states the important results and it omits the proofs.
It consists of eight parts: 1. review of fundamental notions of analysis, 2. differential calculus on Banach spaces, 3. differentiable manifolds, finite dimensional case, 4. integration on manifolds, 5. Riemannian manifolds, Kaehlerian manifolds, 6. connections on a principle fibre bundle, 7. distributions and 8. differentiable manifolds, infinite dimensional case.
The selection of topics and the way they are structured speaks for itself.
I really like this book. It contains all I want and have to learn about mathematics.
What every young (and not so young!) math phys should know August 28, 2008
Mix Master
1 out of 1 found this review helpful
Writing a review for something that everybody knows its high quality would be a waste of time, but perhaps not anymore - younger people should know the 'standard candles'.
Unless you are in a place where all this material you can attend from lectures, this is the book that if you are (or want to be) a mathematical physicist must try to read 'a little every day', hoping that eventually things will start focusing and you will catch up.
It should be considered in a sense as THE modern analogue of Synge & Schild's Tensor Calculus - it has the same selection of topics but now all on manifolds: Analysis on Manifolds, Riemannian geometry, Integration, Connections, plus distributions and aplications to PDEs and selected topics of infinite-dim geometry.
So you have here a source-book that will not only allow you to formulate, in a modern way, physical laws (differential geometry) but also help you to study them (PDEs).
It is a profitable reading for someone who is somewhat versatile with real analysis (say at the level of Haaser & Sullivan) and once you get going, you never stop!
Start off from chapter 3 and get back if you need an explanation of a word you don't understand or have forgotten.
After you have a basic understanding a Riemannian geometry from this book you'll hopefully be able to reach Mme Choquet's new book on GR and the Einstein Equations, it is a continuation and uses the same notation, or volume 2 of the book under review on various topics in mathematical physics.
Most importantly, keep your cool and don't get intimidated!
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