On causal compatibility of quantum field theories and space-times
The author addresses the problem to determine the amount of information concerning the geometric structure, i.e. the existence of spacetime plus metric, encoded in the algebraic structure of the net of local observables. Causal compatibility has been proposed and studied earlier by the author [Rev. Math. Phys. 8, No. 2, 229-270 (1996)]. For a more recent work by the author see [Int. J. Theor. Phys. 37, No. 1, 375-385 (1998; Zbl 0909.46059)]. One main pillar is the striking result that the geometric structure is uniquely determined up to conformal equivalence. The present paper characterizes space-like separation in an algebraic way so as to make sense even in cases of partially ordered sets of algebras for which there is no underlying spacetime. Also, it appears that the general goal is to replace properties of spacetime by those of local nets.
algebraic structure of the net of local observables
scientific article; zbMATH DE number 1316938