An Introduction to Noncommutative Differential Geometry and its Physical Applications
by: J. Madore
* Publisher: Cambridge University Press
* Number Of Pages: 378
* Publication Date: 1999-02-01
* Sales Rank: 827242
* ISBN / ASIN: 0521659914
* EAN: 9780521659918
* Binding: Paperback
* Manufacturer: Cambridge University Press
* Studio: Cambridge University Press
* Average Rating: 5
* Total Reviews: 2
Book Description:
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.
Date: 2000-09-15 Rating: 5
Review:
Very nice, lots of good stuff
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).
Date: 2000-04-30 Rating: 5
Review:
An Introduction to Noncommutative Differential Geometry and
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!
http://ifile.it/i4o7gt/madorintrodnoncodiffeg9.rar
