Local primitive causality and the common cause principle in quantum field theory

Miklós Rédei and Stephen J. Summers

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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 ), φ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A∈ A (V 1 ), B∈ 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 ( A (V 1 ), 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.

Keywords: causality; common cause principle; quantum field theory (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2002
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Foundations of Physics, 2002, 32(3), pp. 335-355. ISSN: 0015-9018

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