arXiv subjects

Koen van den Dungen

Publications and source records attributed to Koen van den Dungen.

20 records · Page 2Linked to original sources

arXiv2012

Particle Physics from Almost Commutative Spacetimes

Our aim in this review article is to present the applications of Connes' noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical audience, in this article we introduce the ideas and concepts from noncommutative geometry using physicists' terminology, gearing towards the predictions that can be derived from the noncommutative description. Focusing on a light package of noncommutative geometry (so-called 'almost commutative manifolds'), we shall introduce in steps: electrodynamics, the electroweak model, culminating in the full Standard Model. We hope that our approach helps in understanding the role noncommutative geometry could play in describing particle physics models, eventually unifying them with Einstein's (geometrical) theory of gravity.

hep-th↗

arXiv2011

Electrodynamics from Noncommutative Geometry

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 manifolds. The most notable example is the derivation of the Standard Model of high energy physics from a suitably chosen almost commutative manifold. In contrast to such a non-abelian gauge theory, it has long been thought impossible to describe an abelian gauge theory within this framework. The purpose of this paper is to improve on this point. We provide a simple example of a commutative spectral triple based on the two-point space, and show that it yields a U(1) gauge theory. Then, we slightly modify the spectral triple such that we obtain the full classical theory of electrodynamics on a curved background manifold.

math-ph↗