Pseudo-Hermitian systems with PT-symmetry: Degeneracy and Krein space
arXiv:1610.08101 · doi:10.1007/s10773-017-3299-5
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 η 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.
arXiv comment13 pages
References in corpus (17)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Making Sense of Non-Hermitian Hamiltonians
- Complex Extension of Quantum Mechanics
- Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
- Pseudo-Hermitian Representation of Quantum Mechanics
- Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
- Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
- Exceptional Points of Non-hermitian Operators
- Exact PT-Symmetry Is Equivalent to Hermiticity
- Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
- Time-Reversal Symmetry in Non-Hermitian Systems
- A New Class of non-Hermitian Quantum Hamiltonians with PT Symmetry
- Consistency of PT-symmetric quantum mechanics
- Is Pseudo-Hermitian Quantum Mechanics an Indefinite-Metric Quantum Theory?
- Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity
- Pseudohermitian Hamiltonians, time-reversal invariance and Kramers degeneracy
- PT-Symmetric Representations of Fermionic Algebras