  Polarization-free generators, i.e. ``interacting'' Heisenberg operators which
are localized in wedge-shaped regions of Minkowski space and generate single
particle states from the vacuum, are a novel tool in the analysis and synthesis
of two-dimensional integrable quantum field theories. In the present article,
the status of these generators is analyzed in a general setting. It is shown
that such operators exist in any theory and in any number of spacetime
dimensions. But in more than two dimensions they have rather delicate domain
properties in the presence of interaction. If, for example, they are defined
and temperate on a translation-invariant, dense domain, then the underlying
theory yields only trivial scattering. In two-dimensional theories, these
domain properties are consistent with non-trivial interaction, but they exclude
particle production. Thus the range of applications of polarization-free
generators seems to be limited to the realm of two-dimensional theories.
