Spectral Theory of Perturbative Decays

We propose a complex approach to evaluating afunction sum of two noncommuting non-Hermitianoperators. We propose an explicit expansion of theevolution operator in the case of the neutral K-mesonsystem influenced by an external interaction. Theimportance is pointed out of considering the algebraicexpansion of the time evolution operator whenever thedynamics decouples the internal transitions andcenter-of-mass motion.