Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties
arXiv:math-ph/0407011 · doi:10.1063/1.1804230
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.
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
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- On the response of a particle detector in Anti-de Sitter spacetime
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- Passive States for Essential Observers
- Holography versus Correspondence principle: eternal Schwarzschild-anti-de Sitter geometry