A simple proof of duality for local algebras in free quantum field theory

DOI10.1063/1.527322zbMath0633.46067OpenAlexW2090517358MaRDI QIDQ3771068

Peter D. Hislop

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1063/1.527322

zbMATH Keywords

cyclicitylocal Sobolev spacesdilatation covarianceduality for local von Neumann algebrasfactor propertyfree-scalar quantum field models with any masspairs of real linear manifolds in the one-particle subspaces of the Fock spacesseparability of the vacuum

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Axiomatic quantum field theory; operator algebras (81T05) Applications of selfadjoint operator algebras to physics (46L60) Miscellaneous applications of functional analysis (46N99)

Related Items (5)

A note on Haag duality ⋮ The decoherence-free subalgebra of Gaussian quantum Markov semigroups ⋮ Twisted duality of the CAR-algebra ⋮ Continuity of Symplectically Adjoint Maps and the Algebraic Structure of Hadamard Vacuum Representations for Quantum Fields on Curved Spacetime ⋮ Nuclearity, split property, and duality for the Klein-Gordon field in curved spacetime

Cites Work

• Modular structure of the local algebras associated with the free massless scalar field theory
• A commutation theorem and duality for free Bose fields
• On local functions of fields
• A bounded operator approach to Tomita-Takesaki theory
• Structure of the algebras of some free systems
• An application of modular Hilbert algebras: Duality for free Bose fields
• On the duality condition for a Hermitian scalar field
• A Lattice of Von Neumann Algebras Associated with the Quantum Theory of a Free Bose Field
• Von Neumann Algebras of Local Observables for Free Scalar Field

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