Carey A. (Ed.) Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory

European Mathematical Society, Switzerland, 2011. —– 281 p. — (EMS, ESI Lectures in Mathematics and Physics) — ISBN: 3037190086.This volume is a collection of expository articles on mathematical topics of current interest that have been partly stimulated or influenced by interactions with physical theory. Some of these articles are based on lectures given at various venues over the last few years, revised and written especially for this volume. They cover a diverse range of mathematical topics stemming from different parts of physics.
The major underlying theme of the volume involves the interactions between physics and number theory. This theme is manifested in two ways, first through the study of Feynman integrals and renormalisation theory, and second, through the application of methods from quantum statistical mechanics. In the former, the work of Bogoliubov–Parasuik–Hepp–Zimmermann (BPHZ) on renormalisation theory gave a method for step by step control of divergences and of their regularisation in Feynman’s approach to perturbative quantum field theory.Introduction Notes on Feynman integrals and renormalization
Introduction to motives. With an appendix by Matilde Marcolli
A short survey on pre-Lie algebras
Divergent multiple sums and integrals with constraints: a comparative study
Spectral triples: examples and index theory