A simple proof of duality for local algebras in free quantum field theory

New and simple proofs of duality for local von Neumann algebras in free-scalar field models associated with a general class of regions in Minkowski space are presented. The proofs are given for both the massive and massless cases and an abstract result of Araki [H. Araki, J. Math. Phys. 4, 1343 (1963)] is assumed. The properties of the local algebras are analyzed using the associated real linear manifolds. Duality is proved in the massive models using elementary properties of Sobolev spaces and in the massless model using dilatation covariance. A proof of the factor property and the cyclicity and separability of the vacuum for these local algebras is also given.