Remarks on the Type of Von Neumann Algebras of Local Observables in Quantum Field Theory

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Abstract
The von Neumann algebras of local observables associated with certain regions of space‐time are believed to be factors. We show that these algebras are not of finite type. The commutant of the tensor product of two semifinite von Neumann algebras is analyzed with the aid of this result. The factors in question have the vacuum state as separating and cyclic vector. It is shown that a factor of type I∞ with I∞ commutant, and a subfactor of type I∞ with I∞ relative commutant have a common separating and cyclic vector. This settles negatively some conjectures aimed at proving that these factors are not of type I. An argument of Araki's showing that the factors associated with certain regions are not of type I is presented in simplified form.

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