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 …

A bstract In the context of the spectral action and the noncommutative geometry approach to
the standard model, we build a model based on a larger symmetry. With this grand symmetry …

We study metric properties stemming from the Connes spectral distance on three types of
non-compact non-commutative spaces which have received attention recently from various …

We explore the geometric implications of introducing a spectral cut-off on compact
Riemannian manifolds. This is naturally phrased in the framework of non-commutative …

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 …

Inspired by regularization in quantum field theory, we study topological and metric properties
of spaces in which a cut-off is introduced. We work in the framework of noncommutative …

We study the metric aspect of the Moyal plane from Connes' noncommutative geometry point
of view. First, we compute Connes' spectral distance associated with the natural isometric …

We discuss the relation between the Wasserstein distance of order 1 between probability
distributions on a metric space, arising in the study of Monge-Kantorovich transport problem …

Within the framework of Connes' noncommutative geometry, the notion of an almost
commutative manifold can be used to describe field theories on compact Riemannian spin …