On one-dimensional integrable quantum systems with infinitely many degrees of freedom

We study one-dimensional quantum systems whose S-operator conserves the incoming momenta and particle identities. A survey of systems with known S-operators and an approach for solving them rigorously are presented, and several problems and conjectures are formulated. Subsequently, this approach is used to arrive at relativistic dynamics whose S-operators are those of the Ising model in the scaling limit and of the Federbush model. An invariance property of the wave and scattering operators is discovered and argued to hold at the classical level, too.