Duality for free Bose fields

Konrad Osterwalder
July 02, 1973
An elementary proof of Araki's duality theorem for free fields is presented. The theorem says that for a certain class of regions $\cal O$ in Minkowski space, the commutant of ${\frak A}({\cal O})$, the von Neumann algebra generated by all observables belonging to measurements within $\cal O$, is exactly ${\frak A}({\cal O}')$, where ${\cal O}'$ is the spacelike separated complement of $\cal O$.

Haag duality, free field theory