An Introduction to Noncommutative Differential Geometry and its Physical Applications (London Mathematical Society Lecture Note Series) [Paperback]

J. Madore (Author)

Book Description

ISBN-10: 0521659914 | ISBN-13: 978-0521659918 | Publication Date: August 13, 1999 | Edition: 2

This is an introduction to noncommutative geometry, with special emphasis on those cases where the structure algebra, which defines the geometry, is an algebra of matrices over the complex numbers. Applications to elementary particle physics are also discussed. This second edition is thoroughly revised and includes new material on reality conditions and linear connections plus examples from Jordanian deformations and quantum Euclidean spaces. Only some familiarity with ordinary differential geometry and the theory of fiber bundles is assumed, making this book accessible to graduate students and newcomers to this field.

Editorial Reviews

Review

"...the author has done a good job of opening the way to understanding a difficult theory...worth a look." MAA Online

"...this book provides an excellent pedagogical introduction to noncommutative geometry for mathematicians as well as physicists. The great number of examples together with the comprehensive references at the end of each chapter lead the reader directly to a large variety of results of recent research." Mathematical Reviews

Book Description

This is an introduction to non-commutative geometry, with special emphasis on those cases where the structure algebra, which defines the geometry, is an algebra of matrices over the complex numbers. Applications to elementary particle physics are also discussed. This second edition is throroughly revised and includes new material on reality conditions and linear connections plus examples from Jordanian deformations and quantum eucidean spaces. Only some familiarity with ordinary differential geometry and the theory of fibre bundles is assumed, making this book accessible to graduate students and newcomers to this field.

Product Details

• Paperback: 380 pages
• Publisher: Cambridge University Press; 2 edition (August 13, 1999)
• Language: English
• ISBN-10: 0521659914
• ISBN-13: 978-0521659918
• Product Dimensions: 9.2 x 6.1 x 0.9 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #380,245 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

14 of 14 people found the following review helpful:

5.0 out of 5 stars Very nice, lots of good stuff, September 14, 2000

By 

Pedro L. Ribeiro "lqp-man" (Cotia, SP Brazil) - See all my reviews
(REAL NAME)   

This review is from: An Introduction to Noncommutative Differential Geometry and its Physical Applications (London Mathematical Society Lecture Note Series) (Paperback)

This book is (partially) the answer to my prays: an introductory book on noncommutative geometry, something I've been waiting since I discovered the topic in Connes' seminal text, which I've also reviewed here. Instead of exposing the historical origins, then firing a goddamn chaingun of advanced topics (something quite fascinating, because of the potential of the theory, but not pedagogical), Madore uses a more friendly way of exposing things, by mantaining a compromise between the most natural motivations to the techniques of the subject and the places where the background needed is not so overwhelming. He do teach much of the background (in the sense that you don't need to master functional analysis, operator algebras and advanced differential geometry), but he goes quite fast on it, requiring a rather mature mathematical mind. As noncommutative geometry is not for the faint of the heart, I guess he's not asking too much after all.

The pedagogy of the book is also benefitted from the post-"Connes' book" evolution of noncommutative geometry, because in 1999 the theory and its (real and potential) applications were a great deal more mature and solid than in 1994. Being this theory a work in progress, the better the math knowledge the reader has, the more he or she will learn from Madore's book, which stands maybe as the only pedagogical exposition of noncommutative geometry (now I'm waiting for the huge book from Garcia-Bondia and his colaborators, to be published by Birkhauser in 2001, hope that it contains more background; it would be very useful for those interested in beginning research on the area).

13 of 13 people found the following review helpful:

5.0 out of 5 stars An Introduction to Noncommutative Differential Geometry and, April 30, 2000

By A Customer

This review is from: An Introduction to Noncommutative Differential Geometry and its Physical Applications (London Mathematical Society Lecture Note Series) (Paperback)

FOR PHYSICIST, I strongly reccomend this book! There are so many physical examples in this book. Always we physicists hate mathamatical proofs like a torture. But this book concentrates applications to physics. If you want to study Noncommutative Geometry as a physicist, this book should be chosen as the first introduction!