Quantum Fields as Pointlike Localized Objects

We show that Wightman fields are always well defined objects at each space-time point in the meaning of sesquilinear forms. These sesquilinear forms “sandwiched” with e^–cH (H is the energy operator) are closable operators. We use these results to extend some assertions of Fredenhagen and Hertel about the recovering of Wightman fields from a Haag -Kastler theory of local observables.