On the statistical independence of algebras of observables

DOI10.1063/1.531812zbMath0899.46054OpenAlexW2021224393WikidataQ60781821 ScholiaQ60781821MaRDI QIDQ4339561

Martin Florig, Stephen Jeffrey Summers

Publication date: 3 November 1998

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531812

zbMATH Keywords

\(C^*\)-algebravon Neumann algebrastatistical independencemultiplicativity\(C^*\)-independence\(W^*\)-independencestrict localitykinematical independenceSchlieder property

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Axiomatic quantum field theory; operator algebras (81T05) Applications of selfadjoint operator algebras to physics (46L60)

Related Items (21)

How device-independent approaches change the meaning of physical theory ⋮ Relativity of quantum states in entanglement swapping ⋮ Independences of operator algebras and joint spectrum of operators ⋮ When are quantum systems operationally independent? ⋮ Operational independence, faithful maps and minimal tensor products ⋮ Modular nuclearity: a generally covariant perspective ⋮ The entanglement of independent quantum systems ⋮ Hilbert C∗$C^*$‐module independence ⋮ Operational independence and tensor products of C*-algebras ⋮ Quantum probability theory ⋮ Subsystems and independence in relativistic microscopic physics ⋮ Independence of group algebras ⋮ Complementarity in quantum systems ⋮ Quantum Information and Relativity: An Introduction ⋮ States on operator algebras and axiomatic system of quantum theory ⋮ Quantum information and relativity theory ⋮ Remarks on causality in relativistic quantum field theory ⋮ Remarks on causality in relativistic quantum field theory ⋮ Connes' embedding problem and Tsirelson's problem ⋮ Two algebraic properties of thermal quantum field theories ⋮ Fermionic systems for quantum information people

Cites Work

• Maximal violation of Bell's inequalities is generic in quantum field theory
• On the independence of local algebras. II
• On the direct product of operator algebras. IV
• On the direkt product of \(W^*\)-factors
• Interpolation by type I factors and the flip automorphism
• Logically independent von Neumann lattices
• Independence of local algebras in quantum field theory
• On the independence of local algebras
• ON THE INDEPENDENCE OF LOCAL ALGEBRAS IN QUANTUM FIELD THEORY
• Topological entropy for appropriately approximated C*-algebrasa)
• An Algebraic Approach to Quantum Field Theory
• Strict Localization

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