2019/12/31 by Bin Gui · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP #math.OA #math.QA
paper · pdf · doi:10.1007/s00023-021-01078-5
published as Ann. Henri Poincaré, 22, 4017-4062 (2021) · 44 pages, to appear in Annales Henri Poincaré. A new section added (Sec. 3), notation changed, Sec. 5 (previously Sec. 4) rewritten, the proofs of the main results of Sec. 6 and Sec. 7 are rewritten
arxiv created 2021/06/22 · arxiv updated 2021/11/16
Given an (irreducible) Mobius covariant net \mathcal A, we prove a Bisognano-Wichmann theorem for its categorical extension \mathscr E^\textrmd associated to the braided C^*-tensor category \textrmRep^\textrmd(\mathcal A) of dualizable (more precisely "dualized") Mobius covariant \mathcal A-modules. As a closely related result, we prove a (modified) Bisognano-Wichmann theorem for any (possibly) non-local extension of \mathcal A obtained by a C^*-Frobenius algebra Q in \textrmRep^\textrmd(\mathcal A). As an application, we discuss the relation between the domains of modular operators and the preclosedness of certain unbounded operators in \mathscr E^\textrmd.