Linear stability of noncommutative spectral geometry

Noncommutative spectral geometry of Riemannian foliations

According to [9, 8], the initial datum of noncommutative differential geometry is a spectral triple (A,H, D) (see Section 3.1 for the definition), which provides a description of the corresponding geometrical space in terms of spectral data of geometrical operators on this space. The purpose of this paper is to construct spectral triples given by transversally elliptic operators with respect to...

The Spectral Action Principle in Noncommutative Geometry and the Superstring

A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all tools of noncommutative geometry. In particular, we apply this to the N = 1 supersymmetric non-linear sigma model and derive an expression for the generalized loop space Dirac operator, in presence of a general background, using canonical quantization. The spectral actio...

Spectral noncommutative geometry and quantization: a simple example

The idea that the geometric structure of physical spacetime could be noncommutative exists in different versions. In some of versions, the noncommutativity of geometry is viewed as a direct effect of quantum mechanics, which disappears in the limit in which we consider processes involving actions much larger than the Planck constant [1]. In the noncommutative geometry approach of Connes et. al....

On Some Aspects of Linear Connections in Noncommutative Geometry

We discuss two concepts of metric and linear connections in noncommutative geometry, applying them to the case of the product of continuous and discrete (two-point) geometry. TPJU 5/95 February 1995 ∗Partially supported by KBN grant 2P 302 103 06

Noncommutative geometry