ON A CLASS OF DISTRIBUTIONS OF INTEREST IN QUANTUM-FIELD THEORY

A class of tempered distributions studied by Araki is considered. Thes e distributions are of interest in quantum field theory since they inc lude certain matrix elements of commutators or anticommutators of loca l quantum field operators. A number of results concerning the null reg ions in spacetime of such distributions are presented, for the cases w hen the null regions are causal complements of closed, convex, causall y complete subsets of spacetime. Applications to quantum field theory are discussed, and some immediate applications to the theory of the Kl ein-Gordon equation and the wave equation are noted. (C) 1998 American Institute of Physics.