Exotic smoothness, noncommutative geometry and particle physics

TL;DR

This paper explores how exotic differential structures on spacetime could influence particle physics, suggesting new geometric objects and phenomena that might arise from such structures within the framework of the standard model.

Contribution

It introduces a model incorporating exotic differential structures into the standard model framework, highlighting potential physical effects of these structures.

Findings

Existence of geometric objects due to exotic structures

Potential physical phenomena from exotic differential structures

Construction of an $SU(3) imes SU(2) imes U(1)$ gauge model

Abstract

We investigate how exotic differential structures may reveal themselves in particle physics. The analysis is based on the A. Connes' construction of the standard model. It is shown that, if one of the copies of the spacetime manifold is equipped with an exotic differential structure, compact object of geometric origin may exist even if the spacetime is topologically trivial. Possible implications are discussed. An $SU(3)\otimes SU(2)\otimes U(1)$ gauge model is constructed. This model may not be realistic but it shows what kind of physical phenomena might be expected due to the existence of exotic differential structures on the spacetime manifold.