Abstract
A class of tempered distributions studied by Araki is considered. These distributions are of interest in quantum field theory since they include certain matrix elements of commutators or anticommutators of local quantum field operators. A number of results concerning the null regions in spacetime of such distributions are presented, for the cases when the null regions are causal complements of closed, convex, causally complete subsets of spacetime. Applications to quantum field theory are discussed, and some immediate applications to the theory of the Klein–Gordon equation and the wave equation are noted.
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