Related papers: Gyros as geometry of the standard model
Using some elementary methods from noncommutative geometry a structure is given to a point of space-time which is different from and simpler than that which would come from extra dimensions. The structure is described by a supplementary…
We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.
We extend the classical general relativistic theory of measurement to include the possibility of existence of higher dimensions. The intrusion of these dimensions in the spacetime interval implies that the inertial mass of a particle in…
The non perturbative guiding center transformation is extended to the relativistic regime and takes into account electromagnetic fluctuations. The main solutions are obtained in covariant form: the gyrating particle and the guiding particle…
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…
In this paper the observational consequence of the cosmological models and the expression for the neoclassical tests, luminosity distance, angular diameter distance and look back time are analyzed in the framework of Lyra geometry. It is…
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…
Efforts have been made recently to reformulate traditional Kaluza-Klein theory by using a generalized definition of a higher-dimensional extended space-time. Both electromagnetism and gravity have been studied in this context. We review…
Geometric $\sigma$-models have been defined as purely geometric theories of scalar fields coupled to gravity. By construction, these theories possess arbitrarily chosen vacuum solutions. Using this fact, one can build a Kaluza--Klein…
We consider a four-dimensional space-time supplemented by two discrete points assigned to a $Z_2$ algebraic structure and develop the formalism of noncommutative geometry. By setting up a generalised vielbein, we study the metric structure.…
A review is given of some 2-dimensional metrics for which noncommutative versions have been found. They serve partially to illustrate a noncommutative extension of the moving-frame formalism. All of these models suggest that there is an…
The Standard Model is based on the gauge invariance principle with gauge group U(1)xSU(2)xSU(3) and suitable representations for fermions and bosons, which are begging for a conceptual understanding. We propose a purely gravitational…
This paper is a sequel to one in which we examined the affine symmetry algebras of arbitrary classical principal chiral models and symmetric space models in two dimensions. It examines the extension of those results in the presence of…
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…
We define a two-dimensional noncommutative space as a limit of finite-matrix spaces which have space-time dimension three. We show that on such space the Grosse-Wulkenhaar (renormalizable) action has natural interpretation as the action for…
We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…
I describe the Kaluza-Klein approach to general relativity of 4-dimensional spacetimes. This approach is based on the (2,2)-fibration of a generic 4-dimensional spacetime, which is viewed as a local product of a (1+1)-dimensional base…
The paper examines the geometrical properties of a six-dimensional Kaluza-Klein type model. They may have an impact on the model of the structure of a neutron and its excited states in the realm of one particle physics. The statistical…
A natural extension of the standard model within non-commutative geometry is presented. The geometry determines its Higgs sector. This determination is fuzzy, but precise enough to be incompatible with experiment.
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…