Modular Theory for the Von Neumann Algebras of Local Quantum Physics

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Modular Theoryand Space - Time Symmetriesr

The Bisognano-Wichmann property on the geometric behavior of the modular group of the von Neumann algebras of local observables associated to wedge regions in Quantum Field Theory is shown to provide an intrinsic suucient criterion for the existence of a covariant action of the (universal covering of) the Poincar e group. In particular this gives, together with our previous results, an intrinsi...

Various topological forms of Von Neumann regularity in Banach algebras

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

Group Cohomology, Modular Theory And Space-Time Symmetries

The Bisognano-Wichmann property on the geometric behavior of the modular group of the von Neumann algebras of local observables associated to wedge regions in Quantum Field Theory is shown to provide an intrinsic suucient criterion for the existence of a covariant action of the (universal covering of) the Poincar e group. In particular this gives, together with our previous results, an intrinsi...

/ 05 01 10 4 v 2 3 F eb 2 00 5 New Constructions in Local Quantum Physics ∗

Among several ideas which arose as consequences of modular localization there are two proposals which promise to be important for the classification and construction of QFTs. One is based on the observation that wedge-localized algebras under certain conditions have particle-like generators with simple properties and the second one uses the structural simplification of wedge-localized algebras ...