相关论文: Distances en geometrie non commutative
We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.
The mathematical apparatus of non commutative geometry and operator algebras which Connes has brought to bear to construct a rational scheme for the internal symmetries of the standard model is presented from the physicist's point of view.…
We show that when non-commutative quantum mechanics is formulated on the Hilbert space of Hilbert-Schmidt operators (referred to as quantum Hilbert space) acting on a classical configuration space, spectral triplets as introduced by Connes…
We investigate whether the identification between Connes' spectral distance in noncommutative geometry and the Monge-Kantorovich distance of order 1 in the theory of optimal transport - that has been pointed out by Rieffel in the…
Connes' non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation…
This text is written for the volume of the school/conference "Noncommutative Geometry 2005" held at IPM Tehran. It gives a survey of methods and results in noncommutative geometry, based on a discussion of significant examples of…
We show that the description of the electroweak interactions based on noncommutative geometry of a continuous and a discrete space gives no special relations between the Higgs mass and other parameters of the model. We prove that there…
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…
We show how the Riemannian distance on $\mathbb{S}^n_{++}$, the cone of $n\times n$ real symmetric or complex Hermitian positive definite matrices, may be used to naturally define a distance between two such matrices of different…
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…
In this paper the model considered by Arkani-Hamed, Cohen and Georgi in the context of (de)constructing dimensions has been studied by making use of non-commutative geometry. The non-commutative geometry provides a natural framework to…
The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces…
During the last two decades Alain Connes developed Noncommutative Geometry (NCG), which allows to unify two of the basic theories of modern physics: General Relativity (GR) and the Standard Model (SM) of Particle Physics as classical field…
A construction of conservation laws for $\sigma$-models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing the ordinary calculus of differential forms with other…
Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an approximation by means of a minimal unital commutative…
In [1], Connes presented axioms governing noncommutative geometry. He went on to claim that when specialised to the commutative case, these axioms recover spin or spin^c geometry depending on whether the geometry is ''real'' or not. We…
In noncommutative geometry, Connes's spectral distance is an extended metric on the state space of a C*-algebra generalizing Kantorovich's dual formula of the Wasserstein distance of order 1 from optimal transport. It is expressed as a…
An introduction is given to some selected aspects of noncommutative geometry. Simple examples in this context are provided by finite sets and lattices. As an application, it is explained how the nonlinear Toda lattice and a discrete time…
We study the Connes spectral distance of quantum states and analyse the nonlocality of a 4D generalized noncommutative phase space. By virtue of the Hilbert-Schmidt operatorial formulation, we obtain the Dirac operator and construct a…
We report on the following highlights from among the many discoveries made in Noncommutative Geometry since year 2000: 1) The interplay of the geometry with the modular theory for noncommutative tori, 2) Advances on the Baum-Connes…