Measurement theory in the Lax-Phillips formalism

It is shown that the application of the Lax-Phillips scattering theory to quantum mechanics provides a natural framework for the realization of the ideas of the "Many-Hilbert-Space" theory of Machida and Namiki to describe the development of decoherence in the process of measurement. We show that if the quantum mechanical evolution is pointwise in time, then decoherence occurs only if the Hamiltonian is time-dependent. If the evolution is not pointwise in time (as in Liouville space), then the decoherence may occur even for closed systems. These conclusions apply as well to the general problem of mixing of states.