Group Cohomology, Modular Theory and Space-time Symmetries

Details Group Cohomology, Modular Theory and Space-time Symmetries Group Cohomology, Modular Theory and Space-time Symmetries

1994-01-18

arxiv.org/abs/funct-an/9401002v1

Reviews Math. Phys. 7 (1995), 57-71

Mathematics

Operator Algebras

18 pages, plain TeX, preprint Roma Tor vergata n. 20 dec. 93

Scientific paper

10.1142/S0129055X95000050

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.

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