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arXiv · 1610.08101

Pseudo-Hermitian systems with PT-symmetry: Degeneracy and Krein space

B. Choutri·O. Cherbal·F. Z. Ighezou·M. Drir
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Abstract

We show in the present paper that pseudo-Hermitian Hamiltonian systems with even PT-symmetry admit a degeneracy structure. This kind of degeneracy is expected traditionally in the odd PT-symmetric systems which is appropriate to the fermions as shown by Jones-Smith and Mathur [1] who extended PT-symmetric quantum mechanics to the case of odd time-reversal symmetry. We establish that the pseudo-Hermitian Hamiltonians with even PT-symmetry admit a degeneracy structure if the operator PT anticommutes with the metric operator {\eta} which is necessarily indefinite. We also show that the Krein space formulation of the Hilbert space is the convenient framework for the implementation of unbroken PT-symmetry. These general results are illustrated with great details for four-level pseudo-Hermitian Hamiltonian with even PT-symmetry.

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B. Choutri, O. Cherbal, F. Z. Ighezou, M. Drir. 2016-10-25. Pseudo-Hermitian systems with PT-symmetry: Degeneracy and Krein space. https://doi.org/10.1007/s10773-017-3299-5

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