Spectral Noncommutative Geometry, Standard Model and all that

Abstract

We review the approach to the standard model of particle interactions based on spectral noncommutative geometry. The paper is (nearly) self-contained and presents both the mathematical and phenomenological aspects. In particular the bosonic spectral action and the fermionic action are discussed in detail, and how they lead to phenomenology. We also discuss the Euclidean vs. Lorentz issues and how to go beyond the standard model in this framework.

Comments: Section 8 rewritten. Review article to appear on the Intenartional Journal of Modern Physics A