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


An Introduction to Noncommutative Spaces and their Geometry



Description 
These lectures notes are an intoduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists. We illustrate applications to YangMills, fermionic and gravity models, notably we describe the spectral action recently introduced by Chamseddine and Connes. We also present an introduction to recent work on noncommutative lattices. The latter have been used to construct topologically nontrivial quantum mechanical and field theory models, in particular alternative models of lattice gauge theory.
Here is the list of sections:
1. Introduction. 2. Noncommutative Spaces and Algebras of Functions. 3. Noncommutative Lattices. 4. Modules as Bundles. 5. The Spectral Calculus. 6. Noncommutative Differential Forms. 7. Connections on Modules. 8. Field Theories on Modules. 9. Gravity Models. 10. Quantum Mechanical Models on Noncommutative Lattices.
Appendices: Basic Notions of Topology. The Gel'fandNaimarkSegal Construction. Hilbert Modules. Strong Morita Equivalence. Partially Ordered Sets. Pseudodifferential Operators 

Similar Books 



Home  Authors  About  Contact Us  Email
Copyright © 20022013 FreeScience.info.
Best viewed with Mozilla 1.X 1024x768
free scientific books
