On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models
Among P-pseudo-Hermitian Hamiltonians H = P⁻¹H†P with real spectra, the ''weakly pseudo-Hermitian'' ones (i.e., those employing non-self-adjoint P ≠ P†) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P ≠...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148972 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862750000636755968 |
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| author | Znojil, M. |
| author_facet | Znojil, M. |
| citation_txt | On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Among P-pseudo-Hermitian Hamiltonians H = P⁻¹H†P with real spectra, the ''weakly pseudo-Hermitian'' ones (i.e., those employing non-self-adjoint P ≠ P†) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P ≠ P†, the current involutive operator of charge C gets complemented by a nonequivalent alternative involutive quasiparity operator Q. We show how, in this language, the standard quantum mechanics is restored via the two alternative inner products in the physical Hilbert space of states, with <ψ₁|PQ|ψ₂> = <ψ1|CP|ψ2>.
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| first_indexed | 2025-12-07T21:03:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148972 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:03:12Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Znojil, M. 2019-02-19T12:18:05Z 2019-02-19T12:18:05Z 2008 On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 25 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81Q10; 47B50 https://nasplib.isofts.kiev.ua/handle/123456789/148972 Among P-pseudo-Hermitian Hamiltonians H = P⁻¹H†P with real spectra, the ''weakly pseudo-Hermitian'' ones (i.e., those employing non-self-adjoint P ≠ P†) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P ≠ P†, the current involutive operator of charge C gets complemented by a nonequivalent alternative involutive quasiparity operator Q. We show how, in this language, the standard quantum mechanics is restored via the two alternative inner products in the physical Hilbert space of states, with <ψ₁|PQ|ψ₂> = <ψ1|CP|ψ2>. This paper is a contribution to the Proceedings of the 3-rd Microconference “Analytic and Algebraic Methods III”. Work supported by GACR, grant Nr. 202/07/1307, Institutional Research Plan AV0Z10480505 and by the MSMT “Doppler Institute” project Nr. LC06002. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models Article published earlier |
| spellingShingle | On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models Znojil, M. |
| title | On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models |
| title_full | On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models |
| title_fullStr | On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models |
| title_full_unstemmed | On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models |
| title_short | On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models |
| title_sort | on the role of the normalization factors κn and of the pseudo-metric p ≠ p† in crypto-hermitian quantum models |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148972 |
| work_keys_str_mv | AT znojilm ontheroleofthenormalizationfactorsκnandofthepseudometricppincryptohermitianquantummodels |