Causal spaces, causal complements and their relations to quantum field theory

In this paper the question is analyzed, how it is possible to reconstruct classical spacetime from the net of local observables of a quantum held theory. To this end different aspects of space-time structure are considered separately. Special attention is drawn to the topological and the causal structure of space-time. Within the scope of causality the differences between causal spaces introduced by Kronheimer and Penrose and causal disjointness relations used in algebraic quantum held theory are considered. Finally we show that the free scaler field on a globally hyperbolic space-time is a special example for our scheme, even if the corresponding Klein-Gordon operator is a Huygens operator.