Book Review: Noncommutative geometry

Review of the Phenomenology of Noncommutative Geometry ∗

We present a pedagogical review of particle physics models that are based on the noncom-mutativity of space-time, [ x µ , x ν ] = iθ µν , with specific attention to the phenomenology these models predict in particle experiments either in existence or under development. We summarize results obtained for high energy scattering such as would occur for example in a future e + e − linear collider wi...

Quasicrystals and geometry: a Book Review

Penrose tilings (Fig. 1) are beautiful. They also suggest significant new mathematics, so it is about time someone wrote a book about them which is readable (in fact, eminently readable) by mathematicians. The book, Quasicrystals and geometry, by Marjorie Senechal, has an even broader goal: to present certain developments in crystallography from the past decade. The developments were generated ...

Noncommutative geometry

Gravity From Noncommutative Geometry

We introduce the linear connection in the noncommutative geometry model of the product of continuous manifold and the discrete space of two points. We discuss its metric properties, de ne the metric connection and calculate the curvature. We de ne also the Ricci tensor and the scalar curvature. We nd that the latter di ers from the standard scalar curvature of the manifold by a term, which migh...

Noncommutative Geometry for Pedestrians∗

A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of space-time and to use it as an ultraviolet regulator. An extensive bibliography has been added containing reference to recent review articles as well as to part of the original literature. LMU-TPW 99-11 ∗Lecure given...