On Causal Compatibility of Quantum Eld Theories and Space-times

In 7] the notion of causal compatibility is introduced as a method to determine the conformal structure of space-time uniquely by the net of observable algebras of a quantum eld theory. In this work some new aspects of causal compatibility are discussed. In particular it is shown that for a given lattice of algebras there exists up to conformal equivalence at most one Lorentzian manifold which is causally compatible. This enhances previous results, where special properties of the index set of the net are used.