Abstract
Abstract The proper meaning of spurious (or unphysical) states in boson mapping theories is discussed. It is emphasized that the spurious states in the generalized Dyson boson mapping for a full fermion space are different from those in the Dyson mapping for a truncated collective fermion subspace. A single- j shell model and an SU(3) model are used to clarify this situation. The numerical results show that the Dyson boson mapping for the collective fermion subspace is quite useful for the description of collective states in a many-fermion Hilbert space.
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