The unifying theme of this book is the interplay among noncommutative geometry, physics,
and number theory. The two main objects of investigation are spaces where both the …

Our aim in this review paper is to present the applications of Connes' noncommutative
geometry to elementary particle physics. Whereas the existing literature is mostly focused on …

This book provides an introduction to noncommutative geometry and presents a number of
its recent applications to particle physics. In the first part, we introduce the main concepts …

Noncommutative geometry, inspired by quantum physics, describes singular spaces by their
noncommutative coordinate algebras and metric structures by Dirac-like operators. Such …

A new candidate of cold dark matter arises by a novel elementary particle model: the
almostcommutative AC-geometrical framework. Two heavy leptons are added to the …

This is a survey of the historical development of the spectral Standard Model and beyond,
starting with the ground breaking paper of Alain Connes in 1988 where he observed that …

I recall some popular models for noncommutative space-time and discuss field theories on
these deformed spaces. This includes classical action functionals and quantum field …

In Iochum et al (2004 J. Math. Phys. 45 5003), Jureit and Stephan (2005 J. Math. Phys. 46
043512), Schücker T (2005 Preprint hep-th/0501181) and Jureit et al (2005 J. Math. Phys …

We study the noncommutative geometry of the Moyal plane from a metric point of view.
Starting from a non-compact spectral triple based on the Moyal deformation A of the algebra …

A new candidate for cold dark matter arises from a novel elementary particle model: the
almost-commutative AC-geometrical framework. Two heavy leptons are added to the …