Mathematical Physics seminar: Local operators in integrable quantum field theories
Integrable models provide simplified examples of quantum field theories with self-interaction. As often in relativistic quantum theory, their local observables are difficult to control mathematically. One either tries to construct pointlike local quantum fields, leading to possibly divergent series expansions, or one defines the local observables indirectly via wedge-local quantities, losing control over their explicit form.We propose a new, hybrid approach: We aim to describe local quantum fields; but rather than exhibiting their n-point functions and verifying the Wightman axioms, we establish them as closed operators affiliated with the net of local von Neumann algebras known from the wedge-local approach. This is shown to work at least in the Ising model.