Home Newsletter
News Books
Welcome to FreeScience.info Language/Lingua

Books 3054
· Book News
· Most clicked
· Least clicked

Search for a Book
HELP US TO HELP YOU
Add a new Book

A Short Survey of Noncommutative Geometry

book
Language:
Author: Alain Connes
Url: http://xxx.lanl.gov/abs/hep-th/0003006
Format: Ps, Pdf
Category: Noncommutative Geometry
Pages: 45
Clicks: 1522

Description
We give a survey of selected topics in noncommutative geometry, with some emphasis on those directly related to physics, including our recent work with Dirk Kreimer on renormalization and the Riemann-Hilbert problem. We discuss at length two issues. The first is the relevance of the paradigm of geometric space, based on spectral considerations, which is central in the theory. As a simple illustration of the spectral formulation of geometry in the ordinary commutative case, we give a polynomial equation for geometries on the four dimensional sphere with fixed volume. The equation involves an idempotent e, playing the role of the instanton, and the Dirac operator D. It expresses the gamma five matrix as the pairing between the operator theoretic chern characters of e and D. It is of degree five in the idempotent and four in the Dirac operator which only appears through its commutant with the idempotent. It determines both the sphere and all its metrics with fixed volume form.

Similar Books
An Introduction to Noncommutative Geometry
Noncommutative Geometry Year 2000
Lectures on graded differential algebras and noncommutative geom
Geometries and Forces
Lectures on Noncommutative Geometry
Lectures on Arithmetic Noncommutative Geometry
An Introduction to Noncommutative Spaces and their Geometry
Hopf algebras in noncommutative geometry
An informal introduction to the ideas and concepts of noncommutative geometry
Noncommutative Geometry, Quantum Fields and Motives
Homological methods in Non-commutative Geometry

Home |  Authors | About | Contact Us |  Email 
 Copyright © 2002-2013 FreeScience.info. 

Best viewed with Mozilla 1.X 1024x768
free scientific books