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

arXivquant-ph/0108023MaRDI QIDQ6501817

Stephen Jeffrey Summers, Miklós Rédei

Abstract: If {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 (A(V_1),A(V_2),phi) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A in A(V_1), B in A(V_2) correlated in the normal state phi 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 (A(V_1),A(V_2),phi) with a locally normal and locally faithful state phi and open bounded V_1 and V_2 satisfies the Weak Reichenbach's Common Cause Principle.

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