  Superselection rules induced by the interaction with the environment are a
basis to understand the emergence of classical observables within quantum
theory. The aim of this article is to investigate the decoherence effects,
which lead to superselection sectors, with the help of exactly soluble
Hamiltonian models. Starting from the examples of Araki and of Zurek more
general models with scattering are presented for which the projection operators
onto the induced superselection sectors do no longer commute with the
Hamiltonian. The example of an environment given by a free quantum field
indicates that infrared divergence plays an essential role for the emergence of
induced superselection sectors. For all models the induced superselection
sectors are uniquely determined by the Hamiltonian, whereas the time scale of
the decoherence depends crucially on the initial state of the total system.
