Quantum Hall Effect and Non-commutative Geometry.- Non-commutative Renormalization.- Non-commutative Fluids.- Heisenberg Spin Chains: From Quantum Groups to Neutron Scattering Experiments.- Non-commutative Geometry and the Spectral Model of Space-time.

This book confirms noncommutative geometry as an increasingly useful tool for the description of intricate condensed matter phenomena. It describes the striking progress recently made in gathering all the interactions and fields of the standard model into a non-commutative geometry on a simple internal space. Coverage also details the very recent technique of renormalization of quantum field theories on non-commutative space-time.