Lax-Phillips scattering theory of a relativistic quantum field theoretical Lee-Friedrichs model and Lee-Oehme-Yang-Wu phenomenology

The scattering theory of Lax and Phillips, originally developed for classical wave equations, has recently been extended to the description of the evolution of resonant states in the framework of quantum theory. The resulting evolution law of the unstable system is that of a semigroup, and the resonant state is a well-defined function in the Lax-Phillips Hilbert space. In this paper we apply this theory to a relativistically covariant quantum field theoretical form of the two (or more) channel relativistic quantum field theoretical form of the Lee model. We show that this theory provides a rigorous underlying basis for the Lee-Oehme-Yang-Wu construction.