2008/01/23 by Robert Strich
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #math-ph #math.MP
paper · pdf · doi:10.1063/1.2838155
published as J.Math.Phys.49:022301,2008 · 27 pages
arxiv created 2008/01/23 · openalex publication_date 2008/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this note is to present a unified approach to the results given by Borchers and Buchholz [“Global properties of vacuum states in de Sitter space,” Ann. Inst. Henri Poincare, Sect. A. 70, 23–40 (1999)] and by Buchholz and Summers [“Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties,” J. Math. Phys. 45, 4810–4831 (2004)] which also covers examples of models not presented in these two papers (e.g., d-dimensional Minkowski space-time for d⩾3). Assuming that a state is passive for an observer traveling along certain (essential) worldlines, we show that this state is invariant under the isometry group, is a temperature equilibrium state for the observer at a temperature uniquely determined by the structure constants of the Lie algebra involved, and fulfills (a variant of) the Reeh-Schlieder property. Also, the modular objects associated with such a state and the observable algebra of an observer are computed and a version of weak locality is examined.