dorsal/arxiv
View SchemaLocal Primitive Causality and the Common Cause Principle in Quantum Field Theory
| Authors | Miklos Redei, Stephen J. Summers |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0108023 |
| URL | https://arxiv.org/abs/quant-ph/0108023 |
| Journal | Found.Phys. 32 (2002) 335-355 |
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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"abstract": "If \\{A(V)\\} is a net of local von Neumann algebras satisfying standard axioms\nof algebraic relativistic quantum field theory and V_1 and V_2 are spacelike\nseparated spacetime regions, then the system (A(V_1),A(V_2),\\phi) is said to\nsatisfy the Weak Reichenbach\u0027s Common Cause Principle iff for every pair of\nprojections A \\in A(V_1), B \\in A(V_2) correlated in the normal state \\phi\nthere exists a projection C belonging to a von Neumann algebra associated with\na spacetime region V contained in the union of the backward light cones of V_1\nand V_2 and disjoint from both V_1 and V_2, a projection having the properties\nof a Reichenbachian common cause of the correlation between A and B. It is\nshown that if the net has the local primitive causality property then every\nlocal system (A(V_1),A(V_2),\\phi) with a locally normal and locally faithful\nstate \\phi and open bounded V_1 and V_2 satisfies the Weak Reichenbach\u0027s Common\nCause Principle.",
"arxiv_id": "quant-ph/0108023",
"authors": [
"Miklos Redei",
"Stephen J. Summers"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"journal_ref": "Found.Phys. 32 (2002) 335-355",
"title": "Local Primitive Causality and the Common Cause Principle in Quantum Field Theory",
"url": "https://arxiv.org/abs/quant-ph/0108023"
},
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