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Overview
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features
* First full treatment of the subject and its applications
* Written by the pioneer of this field
* Broad applications in mathematics
* Of interest across most fields
* Ideal as an introduction and survey
* Examples treated include:
@subbul* the space of Penrose tilings
* the space of leaves of a foliation
* the space of irreducible unitary representations of a discrete group
* the phase space in quantum mechanics
* the Brillouin zone in the quantum Hall effect
* A model of space time
Audience: Graduate students and researchers in mathematics and mathematical physics. Particular appeal for analysts, geometers, and differential geometers; those interested in quantization in physics and mathematics; particle physicists,functional analysts; and algebraists.
Synopsis
Developed by Alain Connes, noncummutative geometry is the set of tools and methods that makes possible the classification and analysis of a broad range of objects beyond the reach of classical methods. This English version of the path-breaking French book on the subject gives the definitive treatment of his revolutionary approach to measure theory, geometry, and mathematical physics. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.
Booknews
Developed by Alain Connes (College de France, Institut des Hautes Etudes Scientifiques, Paris), noncommutative geometry is the set of tools and methods that makes possible the classification and analysis of a broad range of objects beyond the reach of classical methods. This English version (based upon an English translation of the original French edition [1990, InterEditions, Paris], but with more than two-thirds of the material new with this work) gives the definitive treatment of this approach to measure theory, geometry, and mathematical physics. Extensive bibliography. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Editorials
From the Publisher
"...A milestone for mathematics. Connes has created a theory that embraces most aspects of 'classical' mathematics and sets us out on a long and exciting voyage into the world of noncommutative mathematics."The book contains a colourful account of the meaning of the term 'non-commutative space,' based on an extraordinary wealth of examples, including the set of all Penrose tilings, the space of leaves of a foliation, the quantum Hall effect and an intriguing non-commutative model of four-dimensional space-time that reproduces the standard model of elementary particles from quite general considerations...
"The reader of the book should not expect proofs of theorems. This is much more a tapestry of beautiful mathematics and physics which contains material to intrigue readers with any mathematical background. At the same time there is a comprehensive bibliography that will lead the reader straight to the sources and proofs of the results."
--VAUGHAN F.R. JONES, University of California, Berkeley
"This beautiful, ambitious, and erudite book explains, through many examples, the phenomena, tools, and some of the applications of noncommutative geometry...The book is written in a way that anyone can get some of the feeling and ideas of the subject...Connes has accomplished the wonderful feat of explaining in a simple and coherent way 20 years (or so) of his impressive work. I recommend this book most highly.
--Jonathan Block, THE MATHEMATICAL INTELLIGENCER, Vol. 20, No. 1, 1998