Missing the point in noncommutative geometry

Coulomb Potential of a Point Mass in Theta Noncommutative Geometry

Abstract. We investigate the form of the Coulomb potential of a point charge in a noncommutative geometry, using a state of minimal dispersion. We find the deviation of the potential at large distances from the point, distinguishing between coordinate distance and measured distance. Defining the “effective” value of an operator as its expectation value in a minimum dispersion state centered at ...

Noncommutative geometry

Duality in Noncommutative Geometry

The structure of spacetime duality and discrete worldsheet symmetries of compactified string theory is examined within the framework of noncommutative geometry. The full noncommutative string spacetime is constructed using the Fröhlich-Gawȩdzki spectral triple which incorporates the vertex operator algebra of the string theory. The duality group appears naturally as a subgroup of the automorphi...

Riemannian manifolds in noncommutative geometry

We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spinc manifolds; and conversely, in the presence of a spinc structure. We also show how to obtain an analogue of Kasparov's fundamental class for a Riemannian manifold, and the associated notion of Poincaré ...

Gauge Networks in Noncommutative Geometry

We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. The configuration space of quiver representations (modulo equivalence) in the category of finite spectral triples is studied; gauge networks appear as an orthonormal basis in a corresponding Hilbert space. We give many examples of gauge networks, also beyond the well-known s...