Related papers: Spectral Noncommutative Geometry, Standard Model a…

We review the noncommutative approach to the standard model. We start with the introduction if the mathematical concepts necessary for the definition of noncommutative spaces, and manifold in particular. This defines the framework of…

We propose that the fermionic part of the action in the framework of the noncommutative description of the Standard Model is spectral, in an analogous way to the bosonic part of the action that is customary considered as being spectral. We…

I will summarize Noncommutative Geometry Spectral Action, an elegant geometrical model valid at unification scale, which offers a purely gravitational explanation of the Standard Model, the most successful phenomenological model of particle…

The principles of noncommutative geometry impose severe restrictions on the structure of (almost) commutative field theories. The Standard Model fits surprisingly well into the noncommutative framework. Here we overview some universal…

We review the noncommutative spectral geometry, a gravitational model that combines noncommutative geometry with the spectral action principle, in an attempt to unify General Relativity and the Standard Model of electroweak and strong…

We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.

We show how (a slight modification of) the noncommutative geometry bosonic spectral action can be obtained by the cancelation of the scale anomaly of the fermionic action. In this sense the standard model coupled with gravity is induced by…

The derivation of the full Standard Model from noncommutative geometry has been a promising sign for possible applications of the latter in High Energy Physics. Many believe, however, that the Standard Model cannot be the final answer. We…

In a previous paper we developed a formalism to construct (potentially) supersymmetric theories in the context of noncommutative geometry. We apply this formalism to explore the existence of a noncommutative version of the minimal…

This is a brief review where some basic elements of non-commutative geometry are given. The rules and ingredients that enter in the construction of the standard model and grand unification models in non-commutative geometry are summarized.…

We consider aspects of the noncommutative approach to the standard model based on the spectral action principle. We show that as a consequence of the incorporation of the Clifford structures in the formalism, the spectral action contains an…

In this paper I discuss connections between the noncommutative geometry approach to the standard model on one side, and the internal space coming from strings on the other. The standard model in noncommutative geometry is described via the…

Using noncommutative geometry, the standard tools of differential geometry can be extended to a broad class of spaces whose coordinates are noncommuting operators acting on a Hilbert space. In the simplest case of coordinates being matrix…

Noncommutative spectral geometry succeeds in explaining the physics of the Standard Model of electroweak and strong interactions in all its details as determined by experimental data. Moreover, by construction the theory lives at very high…

We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple…

In this publication we present an extension of the Standard Model within the framework of Connes' noncommutative geometry [1]. The model presented here is based on a minimal spectral triple [7] which contains the Standard Model particles,…

A short introduction on elements of noncommutative geometry, which offers a purely geometric interpretation of the Standard Model and implies a higher derivative gravitational theory, is presented. Physical consequences of almost…

Using the formalism of superconnections, we show the existence of a bosonic action functional for the standard K-cycle in noncommutative geometry, giving rise, through the spectral action principle, only to the Einstein gravity and Standard…

A formulation of the non-commutative geometry for the standard model of particle physics with a Lorentzian signature metric is presented. The elimination of the fermion doubling in the Lorentzian case is achieved by a modification of…

This PhD thesis aims at combining the framework of noncommutative geometry and supersymmetry. A particular class of non-commutative geometries called almost-commutative geometries can be used to describe particle theories. This thesis…