Local Primitive Causality and the Common Cause Principle in Quantum Field Theory

Foundations of Physics 32 (3):335-355 (2001)
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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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Miklós Rédei
London School of Economics

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