Worldline fuzziness and spacetime noncommutativity

We here offer a perspective on results obtained in collaboration with Amelino-Camelia and Rosati, which were reported in Refs.[6, 7, 8]. We advocate a formalization of spacetime noncommutativity within the manifestly covariant formulation of quantum mechanics. Using as illustrative example the case of the much-studied κ-Minkowski noncommutative spacetime, we show how such a setup may lead to a crisp characterization of relative locality and of worldline fuzziness in a quantum spacetime.