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

Redei, Miklos and Summers, Stephen J. (2001) Local primitive causality and the common cause principle in quantum field theory. [Preprint]

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    Abstract

    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.


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    Item Type: Preprint
    Keywords: Common cause, quantum field theory
    Subjects: Specific Sciences > Physics > Quantum Field Theory
    Depositing User: Miklos Redei
    Date Deposited: 08 Aug 2001
    Last Modified: 07 Oct 2010 11:10
    Item ID: 352
    URI: http://philsci-archive.pitt.edu/id/eprint/352

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