Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics

Non-Hermitian quantum-Hamiltonian-candidate combination [Formula: see text] of a non-Hermitian unperturbed operator [Formula: see text] with an arbitrary “small” non-Hermitian perturbation [Formula: see text] is given a mathematically consistent unitary-evolution interpretation. The formalism generalizes the conventional constructive Rayleigh–Schrödinger perturbation expansion technique. It is sufficiently general to take into account the well known formal ambiguity of reconstruction of the correct physical Hilbert space of states. The possibility of removal of the ambiguity via a complete, irreducible set of observables is also discussed.