## Local primitive causality and the common cause principle in quantum field theory (2002)

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Venue: | FOUND. PHYS |

Citations: | 7 - 5 self |

### BibTeX

@ARTICLE{Rédei02localprimitive,

author = {Miklós Rédei and Stephen J. Summers},

title = {Local primitive causality and the common cause principle in quantum field theory },

journal = {FOUND. PHYS},

year = {2002},

volume = {32},

number = {3},

pages = {335--355}

}

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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), f) 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 f 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), f) with a locally normal and locally faithful state f and suitable bounded V 1 and V 2 satisfies the