% Encoding: UTF-8
@COMMENT{BibTeX export based on data in FAU CRIS: https://cris.fau.de/}
@COMMENT{For any questions please write to cris-support@fau.de}
@article{faucris.276877966,
abstract = {Motivated by constructions in Algebraic Quantum Field Theory we introduce wedge domains in compactly causal symmetric spaces M=G/H, which includes in particular anti-de Sitter space in all dimensions and its coverings. Our wedge domains generalize Rindler wedges in Minkowski space. The key geometric structure we use is the modular flow on M defined by an Euler element in the Lie algebra of G. Our main geometric result asserts that three seemingly different characterizations of these domains coincide: the positivity domain of the modular vector field, the domain specified by a KMS-like analytic extension condition for the modular flow, and the domain specified by a polar decomposition in terms of certain cones. In the second half of the article we show that our wedge domains share important properties with wedge domains in Minkowski space. If G is semisimple, there exist unitary representations (U, H) of G and isotone covariant nets of real subspaces H(O) subset of H, defined for any open subset O subset of M, which assign to connected components of the wedge domains a standard subspace whose modular group corresponds to the modular f low on M. This corresponds to the Bisognano-Wichmann property in Quantum Field Theory. We also show that the set of G-translates of the connected components of the wedge domain provides a geometric realization of the abstract wedge space introduced by the first author and V. Morinelli.},
author = {Neeb, Karl Hermann and Olafsson, Gestur},
doi = {10.1093/imrn/rnac131},
faupublication = {yes},
journal = {International Mathematics Research Notices},
note = {CRIS-Team WoS Importer:2022-06-17},
peerreviewed = {Yes},
title = {{Wedge} {Domains} in {Compactly} {Causal} {Symmetric} {Spaces}},
year = {2022}
}