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

- Publication Year:
- 2001

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Learn more- Repository URL:
- http://philsci-archive.pitt.edu/id/eprint/352

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##### preprint description

If $\{{\cal A}(V)\}$ 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 $({\cal A}(V_1),{\cal A}(V_2),\phi)$ is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections $A\in{\cal A}(V_1)$, $B\in{\cal A}(V_2)$ 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 $({\cal A}(V_1),{\cal A}(V_2),\phi)$ 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.