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Communications in Mathematical Physics

, Volume 61, Issue 3, pp 267–273 | Cite as

Remarks on the modular operator and local observables

  • Carlo Rigotti
Article

Abstract

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.

Keywords

Neural Network Statistical Physic Field Theory Complex System Quantum Field Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Carlo Rigotti
    • 1
  1. 1.Istituto Matematico “G. Castelnuovo”Università di RomaRomaItaly

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