相关论文: Kaluza-Klein Aspects of Noncommutative Geometry

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.…

Building on the theory of noncommutative complex structures, the notion of a noncommutative K\"ahler structure is introduced. In the quantum homogeneous space case many of the fundamental results of classical K\"ahler geometry are shown to…

The ``Kaluza-Klein-type'' geometric structure appropriate to study the central extension of the Galilei group and non-relativistic physics is reviewed.

It has been shown that the orbits of motion for a wide class of non-relativistic Hamiltonian systems can be described as geodesic flow on a manifold and an associated dual. This method can be applied to a four dimensional manifold of orbits…

In this note the noncommutative geometry is interpreted as a functor, whose range is a family of the operator algebras. Some examples are given and a program is sketched.

Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.

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.

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…

Following the general principles of noncommutative geometry, it is possible to define a metric on the space of pure states of the noncommutative algebra generated by the coordinates. This metric generalizes the usual Riemannian one. We…

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…

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 introduce a class of non-commutative geometries, loosely referred to as para-spaces, which are manifolds equipped with sheaves of non-commutative algebras called para-algebras. A differential analysis on para-spaces is investigated,…

In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics…

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

Various theories of spinning particles are interpreted as realizing elements of an underlying geometric theory. Classical particles are described by trajectories on the Poincare group. Upon quantization an eleven-dimensional Kaluza-Klein…

In this paper we introduce a family of examples that can be regarded as spaces of nonpositive curvature, but with the distinct quality that they are not complete as metric spaces. This amounts to the fact that they are modelled on a finite…

Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie…

Stabilization, by deformation, of the Poincar\'{e}-Heisenberg algebra requires both the introduction of a fundamental lentgh and the noncommutativity of translations which is associated to the gravitational field. The noncommutative…

A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of space-time and to use it as an ultraviolet regulator. An…

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…