Communications in Mathematical Physics

, Volume 110, Issue 2, pp 247–259 | Cite as

Maximal violation of Bell's inequalities is generic in quantum field theory

  • Stephen J. Summers
  • Reinhard Werner


Under weak technical assumptions on a net of local von Neumann algebras {A(O)} in a Hilbert space ℋ, which are fulfilled by any net associated to a quantum field satisfying the standard axioms, it is shown that for every vector state φ in ℋ there exist observables localized in complementary wedge-shaped regions in Minkowski space-time that maximally violate Bell's inequalities in the state φ. If, in addition, the algebras corresponding to wedge-shaped regions are injective (which is known to be true in many examples), then the maximal violation occurs in any state φ on ℬ(ℋ) given by a density matrix.


Neural Network Statistical Physic Hilbert Space Field Theory Complex System 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Stephen J. Summers
    • 1
  • Reinhard Werner
    • 2
  1. 1.Department of MathematicsUniversity of RochesterRochesterUSA
  2. 2.Fachbereich PhysikUniversität OsnabrückOsnabrückFederal Republic of Germany

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