Nonunitary nature of the Dyson boson mapping revisited

The nonunitary character of the Dyson boson mapping is explored in a model case with the monopole pairing interaction. It is shown that because of the very special form of this interaction, the calculations in the intrinsic state formalism with the particle-particle representation of the Hamiltonian reproduce the exact results of the original fermion space. In contrast, we show that with the particle-hole representation of the Hamiltonian the intrinsic state approach produces erroneous results. Of course, upon employing the physical boson states we recover the exact results in the particle-hole represenation as well.