On the Approximation in the Hermitian Treatment of Dyson Boson Expansion Theory

We discuss the Hermitian treatment of the Dyson-type boson expansion theory. We show that the basic assumption of the conventional treatment does not hold in general and that the method is only approximately valid. The exception is the case in which the multi-phonon states are mutually orthogonal, which is not expected in realistic nuclear systems. We also show that the approximation is of the same order as that of the truncation of the expansion usually done in the Hermitian-type boson expansion theory.