String–Localized Fields in a Strongly Nonlocal Model

We study a weakly local, but nonlocal model in spacetime dimension d ≥ 2 which satisfies the remaining Wightman axioms. We prove that this model is (quantitatively) maximally nonlocal; nevertheless, it has string–localized observables of the sort which enable two–body scattering theory to be defined. In two spacetime dimensions, it even has a covariant and local subnet of observables localized in bounded subsets of Minkowski space which has a nontrivial scattering matrix. This model exemplifies the algebraic construction of local observables from algebras associated with strongly nonlocal fields.