 01299 Miklos Redei and Stephen J. Summers
 Local Primitive Causality and the Common Cause Principle in Quantum
Field Theory
(51K, Latex)
Aug 12, 01

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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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