Related papers: Riemannian and Non-commutative Geometry in Physics
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…
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…
We overview a new mechanism whereby classical Riemannian geometry emerges out of the differential structure on quantum spacetime, as extension data for the classical algebra of differential forms. Outcomes for physics include a new formula…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…
In recent years Quantum Superstrings and Quantum Gravity approaches have come to rely on non differenciable spacetime manifolds. These throw up a noncommutative spacetime geometry and we consider the origin of mass and a related…
We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field…
In this work we look for a geometric description of non-gravitational forces. The basic ideas are proposed studying the interaction between a punctual particle and an electromagnetic external field. For this purpose, we introduce the…
Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the…
We provide an intrinsic formulation of the noncommutative differential geometry developed earlier by Chaichian, Tureanu, R. B. Zhang and the second author. This yields geometric definitions of covariant derivatives of noncommutative metrics…
The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly…
These notes aim to give an introduction to a few aspects of noncommutative geometry.
We analyze some extensions of General Relativity. Within the framework of modified gravity, the Newtonian limit of a class of gravitational actions is discussed on the basis of the corresponding scalar-tensor model. For a generalized…
We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime…
The two equations of motion for a test particle are compared with each other. One is in the Non commutative space involving a static rigid sphere (as a source of central force) and the other is in the usual space involving a slowly…
Some results of author's work in a non-geometrical approach to quantum gravity are reviewed here, among them: a quantum mechanism of classical gravity giving a possibility to compute the Newton constant; asymptotic freedom at short…
Noncommutative geometry has become popular mathematics for describing speculative physics beyond the Standard Model. Noncommutative QED has long been known to fit within the framework of the Standard-Model Extension (SME). We argue in this…
In this paper we explain how to define "lower dimensional'' volumes of any compact Riemannian manifold as the integrals of local Riemannian invariants. For instance we give sense to the area and the length of such a manifold in any…
We review quantum gravity model building using the new formalism of `quantum Riemannian geometry' to construct this on finite discrete spaces and on fuzzy ones such as matrix algebras. The formalism starts with a `differential structure' as…
This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…