Adequacy of the boson basis and the identification of spurious states

Abstract

It is shown that it is not necessary to resort to an explicit mapping of the fermion basis into the boson space when bifermion excitations are treated in a boson picture. One may use the usual ideal boson basis in the boson space. Under certain circumstances this may lead to the occurrence of spurious states. However, these do not mix with the physical states and they can be identified by means of a simple procedure which is developed within the framework of the Dyson boson method. The results are illustrated by means of three interesting cases in the Sp(4) model.