Von Neumann Algebras of Local Observables for Free Scalar Field

Abstract

Basic properties of von Neumann algebras of local observables for the free scalar field are investigated. In particular, the duality theorem for regions at a fixed time is proved. It is also shown that von Neumann algebras for regions at a fixed time are factors of type II∞ or III∞. An argument which excludes the possibility of a factor of type I for a general class of theory and for a certain class of regions is given.