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.
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Huzihiro Araki (1964) studied this question.
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