Exact Results in Quantum Theory

I will present some recent joint work with A. Brothier on the construction of a 1+1-dimensional gauge theory by operator-algebraic methods. The construction aims at providing a continuum-limit field algebra starting from a lattice formulation. Furthermore, I will explain how the categorical construction of representations of Thompson’s groups by Jones leads to an automorphic action of said groups on an intermediate field algebra — the semi-continuum field algebra. Supplementing the latter with a state, one expects from a renormalization group perspective to arrive at a notion of continuum field algebra. I will discuss the type of this limit w.r.t. a natural class of states.