相关论文: On noncommutative geometry of the Standard Model: …

A notion of fundamental group of spectral triples has been introduced. The notion uses a noncommutative analogue of unramified coverings. It was shown that in commutative case this fundamental group is a profinite completion of fundamental…

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

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…

Extensions of the Standard Model of elementary particle physics to noncommutative geometries are proposed by string models. Independent of this motivation, one may consider such a model as an effective field theory with higher-dimensional…

I give a summary review of the research program using noncommutative geometry as a framework to determine the structure of space-time. Classification of finite noncommutative spaces under few assumptions reveals why nature chose the…

Recent indications of neutrino oscillations raise the question of the possibility of incorporating massive neutrinos in the formulation of the Standard Model (SM) within noncommutative geometry (NCG). We find that the NCG requirement of…

We give a brief account of the description of the standard model in noncommutative geometry as well as the thermal time hypothesis, questioning their relevance for quantum gravity.

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…

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…

Application of the noncommutative geometry to several physical models is considered.

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 show that allowing the metric dimension of a space to be independent of its KO-dimension and turning the finite noncommutative geometry F-- whose product with classical 4-dimensional space-time gives the standard model coupled with…

This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…

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 mathematical and phenomenological aspects. In particular the bosonic…

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…

Noncommutative geometry, in its many incarnations, appears at the crossroad of various researches in theoretical and mathematical physics: from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and…

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…

The development of Noncommutative Geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and derivation structures that arise in particle and field interactions and fundamental…

Starting from the concept of the universal exterior algebra in non-commutative differential geometry we construct differential forms on the quantum phase-space of an arbitrary system. They bear the same natural relationship to quantum…

Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and General relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the…