Related papers: Noncommutative Spectral Geometry: A Short Review
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…
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…
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…
The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of…
Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum…
Cosmological consequences of the noncommutative geometry spectral action are presented. Neglecting the nonminimal coupling of the Higgs field to the curvature, background cosmology remains unchanged, and only the inhomogeneous perturbations…
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…
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…
In the noncommutative geometry approach to the standard model we discuss the possibility to derive the extra scalar field sv- initially suggested by particle physicist to stabilize the electroweak vacuum - from a "grand algebra" that…
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 review a gravitational model based on noncommutative geometry and the spectral action principle. The space-time geometry is described by the tensor product of a four-dimensional Riemanian manifold by a discrete noncommutative space…
Noncommutative spectral geometry offers a purely geometric explanation for the standard model of strong and electroweak interactions, including a geometric explanation for the origin of the Higgs field. Within this framework, the…
A summary of noncommutative spectral geometry as an approach to unification is presented. The role of the doubling of the algebra, the seeds of quantization and some cosmological implications are briefly discussed.
We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.
We discuss the possibility to extend the spectral action up to energy close to the Planck scale, taking also into account the gravitational effects given by graviton exchange. Including this contribution in the theory, the coupling constant…
In the context of the spectral action and the noncommutative geometry approach to the standard model, we build a model based on a larger symmetry. With this "grand symmetry" it is natural to have the scalar field necessary to obtain the…
In Gen. Rel. Grav. (36, 111-126 (2004); in press, gr-qc/0410010) we have proposed a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry was developed in terms of a noncommutative algebra…
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…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
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…