Wavefront sets in algebraic quantum field theory

The investigation of wavefront sets of n-point distributions in quantum fie ld theory has recently acquired some attention stimulated by results obtain ed with the help of concepts from microlocal analysis in quantum field theo ry in curved spacetime. In the present paper, the notion of wavefront set o f a distribution is generalized so as to be applicable to states and linear functionals on nets of operator algebras carrying a covariant action of th e translation group in arbitrary dimension. In the case where one is given a quantum field theory in the operator algebraic framework, this generalize d notion of wavefront set, called "asymptotic correlation spectrum", is fur ther investigated and several of its properties for physical states are der ived. We also investigate the connection between the asymptotic correlation spectrum of a physical state and the wavefront sets of the corresponding W ightman distributions if there is a Wightman field affiliated to the local operator algebras. Finally we present a new result (generalizing known fact s) which shows that certain spacetime points must be contained in the singu lar supports of the 2n-point distributions of a non-trivial Wightman field.