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