GROUP COHOMOLOGY, MODULAR THEORY AND SPACE-TIME SYMMETRIES
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Publication:4859066
DOI10.1142/S0129055X95000050zbMATH Open0837.46058arXivfunct-an/9401002MaRDI QIDQ4859066
Author name not available (Why is that?)
Publication date: 24 May 1996
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/funct-an/9401002
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