Noncommutative geometry induced by spin effects

Quantum Dissipation Induced Noncommutative Geometry

The quantum statistical dynamics of a position coordinate x coupled to a reservoir requires theoretically two copies of the position coordinate within the reduced density matrix description. One coordinate moves forward in time while the other coordinate moves backward in time. It is shown that quantum dissipation induces, in the plane of the forward and backward motions, a noncommutative geome...

NONCOMMUTATIVE RIEMANNIAN AND SPIN GEOMETRY OF THE STANDARD q-SPHERE

We study the quantum sphere Cq [S] as a quantum Riemannian manifold in the quantum frame bundle approach. We exhibit its 2-dimensional cotangent bundle as a direct sum Ω ⊕ Ω in a double complex. We find the natural metric, volume form, Hodge * operator, Laplace and Maxwell operators. We show that the q-monopole as spin connection induces a natural Levi-Civita type connection and find its Ricci ...

Noncommutative geometry

Gravity From Noncommutative Geometry

We introduce the linear connection in the noncommutative geometry model of the product of continuous manifold and the discrete space of two points. We discuss its metric properties, de ne the metric connection and calculate the curvature. We de ne also the Ricci tensor and the scalar curvature. We nd that the latter di ers from the standard scalar curvature of the manifold by a term, which migh...

Noncommutative Geometry for Pedestrians∗

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 extensive bibliography has been added containing reference to recent review articles as well as to part of the original literature. LMU-TPW 99-11 ∗Lecure given...