MODULAR THEORY AND GEOMETRY

DOI10.1142/S0129055X0000006XzbMath0969.81035arXivmath-ph/9809003OpenAlexW2016307323MaRDI QIDQ4519833

Hans-Werner Wiesbrock, Bert Schroer

Publication date: 4 December 2000

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

Full work available at URL: https://arxiv.org/abs/math-ph/9809003

zbMATH Keywords

modular theoryfinite-dimensional geometrical actionsinfinite-dimensional hidden symmetries

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Applications of operator theory in the physical sciences (47N50) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Axiomatic quantum field theory; operator algebras (81T05) Applications of functional analysis in quantum physics (46N50) Operator algebra methods applied to problems in quantum theory (81R15)

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Cites Work

• Symmetries and modular intersections of von Neumann algebras
• The CPT-theorem in two-dimensional theories of local observables
• Modular intersections of von Neumann algebras in quantum field theory
• Extensions of conformal nets and superselection structures
• Motivations and physical aims of algebraic QFT
• Conformal quantum field theory and half-sided modular inclusions of von- Neumann-algebras
• A note on essential duality
• When does Lorentz invariance imply wedge duality?
• Modular inclusion, the Hawking temperature, and quantum field theory in curved spacetime
• Conformal Haag-Kastler nets, pointlike localized fields and the existence of operator product expansions
• Half-sided modular inclusion and the construction of the Poincaré group
• On the equilibrium states in quantum statistical mechanics
• HAAG DUALITY IN CONFORMAL QUANTUM FIELD THEORY
• On the duality condition for a Hermitian scalar field