Related papers: Riemannian and Non-commutative Geometry in Physics
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
When joined the unified gauge picture of fundamental interactions, the gravitation theory leads to geometry of a space-time which is far from simplicity of pseudo-Riemannian geometry of Einstein's General Relativity. This is geometry of the…
A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell…
The development of Noncommutative Geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and derivation structures that arise in particle and field interactions and fundamental…
The commutative algebra of functions on a manifold is extended to a noncommutative algebra by considering its tensor product with the algebra of nxn complex matrices. Noncommutative geometry is used to formulate an extension of the…
We extend the non-commutative coordinates relationship into other than the Minkowski space-time. We clarify the non-commutativity dependency to the geometrical structure. As well as, we find an inverse map between Riemann's normal and…
The gravitation equations of the general relativity, written for Riemannian space-time geometry, are extended to the case of arbitrary (non-Riemannian) space-time geometry. The obtained equations are written in terms of the world function…
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…
Gravity with incorporation of additional dimensions and noncommutative geometry.
We review the noncommutative spectral geometry, a gravitational model that combines noncommutative geometry with the spectral action principle, in an attempt to unify General Relativity and the Standard Model of electroweak and strong…
It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
A detailed study is made of the noncommutative geometry of $R^3_q$, the quantum space covariant under the quantum group $SO_q(3)$. For each of its two $SO_q(3)$-covariant differential calculi we find its metric, the corresponding frame and…
Equations of spinning objects are obtained in Absolute Parallelism Geometry [AP], a special class of non-Riemannian geometry admitting an alternative non-vanishing curvature and torsion simultaneously. This new set of equations is the…
This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains,…
Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There…
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.
The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of…
We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector…
We construct spectral triples in a sense of noncommutative differential geometry, associated with a Riemannian foliation on a compact manifold, and describe its dimension spectrum.