Von Neumann Algebras and Quantum Field Theory

Von Neumann algebras were originally designed as a framework for various subjects, a major motivation coming from quantum theory. Although von Nuemann algebras have since turned out to have unexpected connections with many different fields, the contact with quantum physics has remained constant and fruitful. I will try to give an account of a recent interplay between quantum field theory and inclusions of von Nuemann algebras. The latter may arise for example as inclusions of local observable algebras, a structure analyzed earlier [10], [13], [39]–[42] and still productive. Here however I will deal with inclusions associated with superselection sectors [11], a setting related to index theory [36] along a line of research I have been following during about the last six years.