Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity

Details Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity

2006-06-21

arxiv.org/abs/quant-ph/0606173v2

Czech J. Phys. 56, 919-933 (2006)

Physics

Quantum Physics

published version, 17 pages

Scientific paper

10.1007/s10582-006-0388-8

Emphasizing the physical constraints on the formulation of a quantum theory based on the standard measurement axiom and the Schroedinger equation, we comment on some conceptual issues arising in the formulation of PT-symmetric quantum mechanics. In particular, we elaborate on the requirements of the boundedness of the metric operator and the diagonalizability of the Hamiltonian. We also provide an accessible account of a Krein-space derivation of the CPT-inner product that was widely known to mathematicians since 1950's. We show how this derivation is linked with the pseudo-Hermitian formulation of PT-symmetric quantum mechanics.

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