ON THE CAUSAL-STRUCTURE OF MINKOWSKI SPACETIME

The causal structure of Minkowski spacetime M is discussed, in terms o f the notions of causal complementation and causal completion. These g eometric notions are relevant for quantum field theory and the theory of the Klein-Gordon equation. Particular attention is given to closed, convex, causally complete subsets of M, and the properties of such se ts are discussed. The study of such sets is motivated by potential app lications to the theory of local nets of von Neumann algebras. The not ion of the envelope of uniqueness of a subset of M, familiar from the theory of the wave equation, is discussed, and some results about the relation of this envelope to the causal completion of the set are pres ented. (C) 1997 American Institute of Physics.