ASYMPTOTIC FIELDS IN SOME MODELS OF QUANTUM FIELD THO ELD THEORY .2.

A quantum field with nonlocal but translation-invariant interaction is considered. We prove that, with a proper smoothness condition on the interaction, the asymptotic limits of the annihilation-creation operators exists. The asymptotic limits are then used to prove that the state space decomposes as a tensor product of an incoming (outgoing) Fock space and a zero-particle space.