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

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

2001-08-06

arxiv.org/abs/quant-ph/0108023v1

Found.Phys. 32 (2002) 335-355

Physics

Quantum Physics

14 pages, Latex

Scientific paper

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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