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In quantum field theory, the rigorous construction of local observables inthe presence of nontrivial interaction is a crucial problem. In a class ofintegrable quantum field theories, a very abstract existence proof has recentlybeen given by Lechner. We give an explicit characterization of these localobservables in terms of the properties of the coefficient functions in anexpansion by interacting creators and annihilators. Some results on theoperator domains of these local observables are given. Using these, weconstructed explicit examples of local observables in the quantum Ising model.

A Characterization Theorem for Local Operators in Factorizing Scattering Models