Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties
Abstract
If a state is passive for uniformly accelerated observers in n-dimensional anti-de Sitter space-time (i.e. cannot be used by them to operate a perpetuum mobile), they will (a) register a universal value of the Unruh temperature, (b) discover a PCT symmetry, and (c) find that observables in complementary wedge-shaped regions necessarily commute with each other in this state. The stability properties of such a passive state induce a "geodesic causal structure" on AdS and concommitant locality relations. It is shown that observables in these complementary wedge-shaped regions fulfill strong additional independence conditions. In two-dimensional AdS these even suffice to enable the derivation of a nontrivial, local, covariant net indexed by bounded spacetime regions. All these results are model-independent and hold in any theory which is compatible with a weak notion of space-time localization. Examples are provided of models satisfying the hypotheses of these theorems.
Keywords
Cite
@article{arxiv.math-ph/0407011,
title = {Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties},
author = {Detlev Buchholz and Stephen J. Summers},
journal= {arXiv preprint arXiv:math-ph/0407011},
year = {2009}
}
Comments
27 pages, 1 figure: dedicated to Jacques Bros on the occasion of his 70th birthday. Revised version: typos corrected; as to appear in J. Math. Phys