Isaac Newton Institute for Mathematical Sciences

Distance in Noncommutative Geometry

Author: Pierre Martinetti (Università di Roma, "La Sapienza")

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.

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