Title

Group Cohomology, Modular Theory And Space-Time Symmetries

Author(s)/Creator(s)

R. Brunetti, Syracuse University, Department of PhysicsFollow
D. Guido, Universita di Roma, Tor Vergata, Dipartimento di MatamaticaFollow
R. Longo, Accademia Nazionale dei Lincei, Centro Lincero InterdisciplinareFollow

Document Type

Article

Date

1994

Keywords

group cohomology, modular theory, space-time symmetries, von Neumann algebras, extensions

Language

English

Disciplines

Mathematics

Description/Abstract

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 sufficient 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 intrinsic characterization of positive-energy conformal pre-cosheaves of von Neumann algebras. To this end we adapt to our use Moore theory of central extensions of locally compact groups by polish groups, selecting and making an analysis of a wider class of extensions with natural measurable properties and showing henceforth that the universal covering of the Poincar'e group has only trivial central extensions (vanishing of the first and second order cohomology) within our class.

Recommended Citation

Brunetti, R.; Guido, D.; and Longo, R., "Group Cohomology, Modular Theory And Space-Time Symmetries" (1994). Physics - All Scholarship. 3.
https://surface.syr.edu/phy/3

Source

Arxiv.org