The Hilbert-Space Structure of Non-Hermitian Theories with Real Spectra*

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We investigate the quantum-mechanical interpretation of models with non-Hermitian Hamiltonians and real spectra. After describing a general framework to reformulate such models in terms of Hermitian Hamiltonians defined on the Hilbert space L2(−∞, ∞), we discuss the significance of the algebra of physical observables.

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