Non-Hermiticity, Boson Realizations, and the Role of a Physical Subspace*

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I give a brief review of boson realizations in quantum many-body theory and how the Dyson-Maleev type mappings give rise to quasi- (or pseudo-) Hermitian structures. In this context it is emphasised that non-Hermiticity of a mapped Hamiltonian is directly linked to a choice of basis states (or the implied inner product). The role of a physical subspace and the necessity to have a formalism which can identify this subspace is highlighted.

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