Stable Quantum Systems in Anti–de Sitter Space: Causality, Independence and Spectral Properties
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چکیده
If a state is passive for uniformly accelerated observers in n-dimensional (n ≥ 2) 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.
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تاریخ انتشار 2004