Deformations of Differential Calculi

TL;DR

This paper explores the relationship between quantum gravitational fluctuations leading to noncommutative geometries and the phenomenological double-sheeted structure suggested by the Standard Model, analyzing their potential connection.

Contribution

It investigates whether the double-sheeted structure observed in the Standard Model can be viewed as a singular limit of a noncommutative Kaluza-Klein theory derived from quantum gravity effects.

Findings

Double-sheeted structure can be considered as a limit of noncommutative geometry models.

Potential link between quantum gravity-induced noncommutative geometries and Standard Model phenomenology.

Analysis of the conditions under which these structures relate.

Abstract

It has been suggested that quantum fluctuations of the gravitational field could give rise in the lowest approximation to an effective noncommutative version of Kaluza-Klein theory which has as extra hidden structure a noncommutative geometry. It would seem however from the Standard Model, at least as far as the weak interactions are concerned, that a double-sheeted structure is the phenomenologically appropriate one at present accelerator energies. We examine here to what extent this latter structure can be considered as a singular limit of the former.