Abstract
If \(\mathcal{A}\)(V) is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V 1 and V 2 are spacelike separated spacetime regions, then the system (\(\mathcal{A}\)(V 1 ), \(\mathcal{A}\)(V 2 ), φ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A∈\(\mathcal{A}\)(V 1 ), B∈\(\mathcal{A}\)(V 2 ) correlated in the normal state φ there exists a projection C belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V 1 and V 2 and disjoint from both V 1 and V 2 , a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system (\(\mathcal{A}\)(V 1 ), \(\mathcal{A}\)(V 2 ), φ) with a locally normal and locally faithful state φ and suitable bounded V 1 and V 2 satisfies the Weak Reichenbach's Common Cause Principle.
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Rédei, M., Summers, S.J. Local Primitive Causality and the Common Cause Principle in Quantum Field Theory. Foundations of Physics 32, 335–355 (2002). https://doi.org/10.1023/A:1014869211488
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DOI: https://doi.org/10.1023/A:1014869211488