A pedagogical and self-contained introduction to noncommutative quantum field theory is
presented, with emphasis on those properties that are intimately tied to string theory and …

Horizon-scale images of black holes (BHs) and their shadows have opened an
unprecedented window onto tests of gravity and fundamental physics in the strong-field …

We render a thorough, physicist's account of the formulation of the Standard Model (SM) of
particle physics within the framework of noncommutative differential geometry (NCG). We …

These lecture notes are an introduction to several ideas and applications of noncommutative
geometry. It starts with a not necessarily commutative but associative algebra which is …

It is known that the spin structure on Riemannian manifold can be extended to
noncommutative geometry using the notion of spectral triple. For finite geometries, the …

In this paper we study the structure of the Hilbert space for the recent noncommutative
geometry models of gauge theories. We point out the presence of unphysical degrees of …

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 …

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 …

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 …

Einstein derived general relativity from Riemannian geometry. Connes extends this
derivation to noncommutative geometry and obtains electro–magnetic, weak, and strong …