Model In Noncommutative Geometry Research Articles

Gravity from non-commutative geometry

We introduce the linear connection in the non-commutative geometry model of the product of continuous manifold and the discrete space of two points. We discuss its metric properties, define the metric connection and calculate the curvature. We define also the Ricci tensor and the scalar curvature. We find that the latter differs from the standard scalar curvature of the manifold by a term, which might be interpreted as the cosmological constant, and apart from that we find no other dynamic fields in the model. Finally we discuss an example solution of flat linear connection, with the non-trivial scaling dependence of the metric tensor on the discrete variable. We interpret the obtained solution as confirmed by the standard model, with the scaling factor corresponding to the Weinberg angle.

Parameter restrictions in a non-commutative geometry model do not survive standard quantum corrections

We have investigated the standard one-loop quantum corrections for a particularly simple non-commutative geometry model containing fermions interacting with a unique abelian gauge field and a unique scalar through Yukawa couplings. In this model there are certain relations among the different coupling constants quite similar to the ones appearing in the Connes-Lott version of the standard model. We find that it is not possible to implement those relations in a renormalization-group invariant way.

Remarks on Alain Connes' approach to the standard model in non-commutative geometry

Our 1992 remarks about Alain Connes' interpretation of the standard model within his theory of non-commutative riemannian spin manifolds.

Noncommutative geometry model for closed bosonic strings.

We show how Witten’s noncommutative geometry may be extended to describe the closed bosonic string. An explicit representation of the ∮ and * product for closed strings is provided.Received 20 August 1986DOI:https://doi.org/10.1103/PhysRevLett.58.1304©1987 American Physical Society