Related papers: A Note on Quantum Odometers
In recent years, several quantizations of real manifolds have been studied, in particular from the point of view of Connes' noncommutative geometry. Less is known for complex noncommutative spaces. In this paper, we review some recent…
We investigate the geode and some of its generalizations from the point of view on noncommutative symmetric functions.
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss--Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of…
Application of the noncommutative geometry to several physical models is considered.
I discuss examples where basic structures from Connes' noncommutative geometry naturally arise in quantum field theory. The discussion is based on recent work, partly collaboration with J. Mickelsson.
We review the notion of submanifold algebra, as introduced by T. Masson, and discuss some properties and examples. A submanifold algebra of an associative algebra $A$ is a quotient algebra $B$ such that all derivations of $B$ can be lifted…
Motivated by the search for new examples of ``noncommutative manifolds'', we study the noncommutative geometry (in the sense of Connes) of the group C*-algebra of the three dimensional discrete Heisenberg group. We present a unified…
We discuss some exact Seiberg--Witten-type maps for noncommutative electrodynamics. Their implications for anomalies in different (noncommutative and commutative) descriptions are also analysed.
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
In this letter we investigate some aspects of the noncommutative differential geometry based on derivations of the algebra of endomorphisms of an oriented complex hermitian vector bundle. We relate it, in a natural way, to the geometry of…
We introduce a family of dense subalgebras of the Toeplitz algebra and give conditions under which our algebras are quasi-free. As a corollary, we show that the smooth Toeplitz algebra introduced by Cuntz is quasi-free.
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 introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out…
In this paper, we study the differential smoothness of diffusion algebras.
We review basic notions and methods of noncommutative geometry and their applications to analysis and geometry on foliated manifolds.
It is well known that noncommutative geometry naturally emerges in the quantum Hall states due to the presence of strong and constant magnetic fields. Here, we discuss the underlying noncommutative geometry of quantum Hall fluids in which…
These notes concern the nonlinear geometry of Banach spaces, asymptotic uniform smoothness and several Banach-Saks-like properties. We study the existence of certain concentration inequalities in asymptotically uniformly smooth Banach…
We discuss quantum deformation of the affine transformation algebra. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators.
We briefly describe how to introduce the basic notions of noncommutative differential geometry on the 3-dim quantum space covariant under the quantum group of rotations $SO_q(3)$.