dorsal/arxiv
View SchemaKrein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity
| Authors | Ali Mostafazadeh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606173 |
| URL | https://arxiv.org/abs/quant-ph/0606173 |
| DOI | 10.1007/s10582-006-0388-8 |
| Journal | Czech J. Phys. 56, 919-933 (2006) |
Abstract
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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"abstract": "Emphasizing the physical constraints on the formulation of a quantum theory\nbased on the standard measurement axiom and the Schroedinger equation, we\ncomment on some conceptual issues arising in the formulation of PT-symmetric\nquantum mechanics. In particular, we elaborate on the requirements of the\nboundedness of the metric operator and the diagonalizability of the\nHamiltonian. We also provide an accessible account of a Krein-space derivation\nof the CPT-inner product that was widely known to mathematicians since 1950\u0027s.\nWe show how this derivation is linked with the pseudo-Hermitian formulation of\nPT-symmetric quantum mechanics.",
"arxiv_id": "quant-ph/0606173",
"authors": [
"Ali Mostafazadeh"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s10582-006-0388-8",
"journal_ref": "Czech J. Phys. 56, 919-933 (2006)",
"title": "Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity",
"url": "https://arxiv.org/abs/quant-ph/0606173"
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