Due to the limited capabilities of current web clients to display formulas I will refer for further details to my papers. Some of them you can download if you click on an icon in the following list. M. Keyl, Causal spaces, causal complements and their relations to quantum field theory, Rev. Math. In this paper the question is analyzed, how it is possible to reconstruct classical space-time from the net of local observables of a quantum field 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 field theory are considered. If you want a reprint of this paper click here to send me a mail. M. Keyl, Quantum field theory and the geometric structure of Kaluza Klein space-time, submitted to Class. The dimensional reduced theories are constructed and the question is considered whether the extended space-time can be reconstructed from them. Click here to get a copy of this paper.