by bounded spacetime regions. We also explain how known examples of quantum fields on AdS fit into our scheme.

The primary lesson to be drawn from this paper is the observation that covariance and passivity properties of states induce strong algebraic relations between the observables, which may be interpreted as manifestations of Einstein causality. In our research program, the theories on AdS treated here serve as a theoretical laboratory to test this striking feature. But the insight gained in this analysis goes beyond this class of field theoretical models to quantum fields on other space–times. Further, it seems to be of relevance in the discussion of causality problems appearing in nonlocal theories, such as string theory and quantum field theory on noncommutative space–times.

Unruh effect, PCT symmetry and weak locality {#main}
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We now enter into the analysis of the implications of our standing assumptions (i)–(iv) by appealing to a deep result of Pusz and Woronowicz for general quantum dynamical systems [@PuWo]. In the present context this result says that the vacuum vector $\Omega$ is, as a consequence of its passivity and mixing properties, invariant under the dynamics of any of the observers discussed above [@PuWo Theorem 1.1]. In particular, 