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Lax-Phillips Scattering Theory of a Relativistic Quantum Field Theoretical Lee-Friedrichs Model and Lee-Oehme-Yang-Wu Phenomenology

The one-channel Wigner-Weisskopf survival amplitude may be dominated by exponential type decay in pole approximation at times not too short or too long, but, in the two channel case, for example, the pole residues are not orthogonal, and the pole approximation evolution does not correspond to a semigroup (experiments on the decay of the neutral K-meson system support the semigroup evolution postulated by Lee, Oehme and Yang, and Yang and Wu, to very high accuracy). The scattering theory of Lax and Phillips, originally developed for classical wave equations, has been recently 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 funtion in the Lax-Phillips Hilbert space. In this paper we apply this theory to relativistically covarant quantum field theoretical form of the (soluble) Lee model. We show that this theory provides a rigorous underlying basis for the Lee-Oehme-Yang-Wu construction.