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Foundations of Physics

, Volume 42, Issue 2, pp 241–255 | Cite as

Reichenbach’s Common Cause Principle in Algebraic Quantum Field Theory with Locally Finite Degrees of Freedom

  • Gábor Hofer-Szabó
  • Péter Vecsernyés
Article

Abstract

In the paper it will be shown that Reichenbach’s Weak Common Cause Principle is not valid in algebraic quantum field theory with locally finite degrees of freedom in general. Namely, for any pair of projections A, B supported in spacelike separated double cones \({\mathcal{O}}_{a}\) and \({\mathcal{O}}_{b}\), respectively, a correlating state can be given for which there is no nontrivial common cause (system) located in the union of the backward light cones of \({\mathcal{O}}_{a}\) and \({\mathcal{O}}_{b}\) and commuting with the both A and B. Since noncommuting common cause solutions are presented in these states the abandonment of commutativity can modulate this result: noncommutative Common Cause Principles might survive in these models.

Keywords

Algebraic quantum field theory Reichenbach’s Common Cause Principle Ising model 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of LogicEötvös UniversityBudapestHungary
  2. 2.Research Institute for Particle and Nuclear PhysicsBudapestHungary

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