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Remarks on the modular operator and local observables

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In this paper we give a characterization of the modular group of a von Neumann algebra ℛ, with a cyclic and separating vector, which provides at the same time a necessary and sufficient condition so that two von Neumann algebras ℛ1 and ℛ2, such that ℛ1⊂ℛ′2, are the mutual commutants, i.e. ℛ1=ℛ′2.

An application is made to the duality property in Quantum Field Theory, and we give a sufficient condition for PCT invariance in a theory of local observables.

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Communicated by R. Haag

Partially supported by C.N.R.

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Rigotti, C. Remarks on the modular operator and local observables. Commun.Math. Phys. 61, 267–273 (1978). https://doi.org/10.1007/BF01940769

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  • DOI: https://doi.org/10.1007/BF01940769

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