### Abstract

We shall present an overview of the distance formula in Noncommutative Geometry. In particular we will recall how gauge fields - including a scalar component - naturally acquire a metric interpretation. This will be illustrated on the one side by the Higgs field in the standard model, on the other side by connection 1-forms on fibre bundles. In particular we will analyse the link between the distance coming from Noncommutative Geometry and another distance classically associated to connections, namely the Carnot-Caratheodory (or horizontal) distance.

### Related Links

- http://fr.arxiv.org/abs/hep-th/0506147 - Carnot-Carathéodory distance and gauge fluctuation in NCG
- http://fr.arxiv.org/abs/hep-th/0104108 - Metric interpretation of the Higgs field
- http://fr.arxiv.org/abs/hep-th/0603051 - Non technical version of the first paper