Related papers: Connes' Model Building Kit
This is a compilation of some well known propositions of Alain Connes concerning the use of noncommutative geometry in mathematical physics.
This text is an introduction to a few selected areas of Alain Connes' noncommutative geometry written for the volume of the school/conference "Noncommutative Geometry 2005" held at IPM Tehran. It is an expanded version of my lectures which…
Application of the noncommutative geometry to several physical models is considered.
I give a summary of the progress made on using the elegant construction of Alain Connes noncommutaive geometry to explore the nature of space-time at very high energies. In particular I show that by making very few natural and weak…
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.…
Connes' noncommutative approach to the standard model of electromagnetic, weak and strong forces is sketched as well as its unification with general relativity.
This is a short survey of some aspects of Alain Connes' contributions to cyclic cohomology theory in the course of his work on noncommutative geometry over the past 30 years.
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…
Quantum groups and quantum homogeneous spaces - developed by several authors since the 80's - provide a large class of examples of algebras which for many reasons we interpret as `coordinate algebras' over noncommutative spaces. This…
Alain Connes' Non-Commutative Geometry program [Connes 1994] has been recently carried out [Prodan, Leung, Bellissard 2013, Prodan, Schulz-Baldes 2014] for the entire A- and AIII-symmetry classes of topological insulators, in the regime of…
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…
A consequence of the Gauss Bonnet theorem is interpreted in term of operator theory by Alain Connes in his book, Non Commutative geometry. In this note we explain in details about his method. We also introduce an operator theoretical nature…
I discuss examples where basic structures from Connes' noncommutative geometry naturally arise in quantum field theory. The discussion is based on recent work, partly collaboration with J. Mickelsson.
The formalism of non-commutative geometry of A. Connes is used to construct models in particle physics. The physical space-time is taken to be a product of a continuous four-manifold by a discrete set of points. The treatment of Connes is…
This article is an introductory survey of index theory in the context of noncommutative geometry, written for the occasion of the 70th birthday of Alain Connes.
An intersection of Noncommutative Geometry and Loop Quantum Gravity is proposed. Alain Connes' Noncommutative Geometry provides a framework in which the Standard Model of particle physics coupled to general relativity is formulated as a…
This is a survey of some recent advances in the theory of singular traces in which the authors have played some part and which were inspired by questions raised by the book of Alain Connes (Noncommutative Geometry, Academic Press 1994).…
We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from…
Noncommutative geometry applied to the standard model of electroweak and strong interactions was shown to produce fuzzy relations among masses and gauge couplings. We refine these relations and show then that they are exhaustive.
Alain Connes' noncommutative theory led to an interesting model including both Standard Model of particle physics and Euclidean Gravity. Nevertheless, an hyperbolic version of the gravitational part would be necessary to make physical…