  We apply the quantum Lax-Phillips scattering theory to a relativistically
covariant quantum field theoretical form of the (soluble) Lee model. We
construct the translation representations with the help of the wave operators,
and show that the resulting Lax-Phillips $S$-matrix is an inner function (the
Lax-Phillips theory is essentially a theory of translation invariant
subspaces). We then discuss the non-relativistic limit of this theory, and show
that the resulting kinematic relations coincide with the conditions required
for the Galilean description of a decaying system.
