On the Role of the Normalization Factors $κ_n$ and of the Pseudo-Metric ${\cal P} \neq {\cal P}^\dagger$ in Crypto-Hermitian Quantum Models
| dc.creator | Znojil, Miloslav | |
| dc.date | 2007-10-24 | |
| dc.date | 2008-01-02 | |
| dc.date.accessioned | 2026-07-07T09:34:47Z | |
| dc.date.available | 2026-07-07T09:34:47Z | |
| dc.description | Among ${\cal P}$-pseudo-Hermitian Hamiltonians $H ={\cal P}^{-1} H^\dagger \cal P}$ with real spectra, the ''weakly pseudo-Hermitian" ones (i.e., those employing non-self-adjoint ${\cal P} \neq {\cal P}^\dagger$) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever ${\cal P} \neq {\cal P}^\dagger$, the current involutive operator of charge ${\cal C}$ gets complemented by a nonequivalent alternative involutive quasiparity operator ${\cal Q}$. 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 $<ψ_1|{\cal PQ}|ψ_2>=< ψ_1|{\cal CP}|ψ_2>$. | |
| dc.description | This is a contribution to the Proc. of the 3-rd Microconference "Analytic and Algebraic Methods III"(June 19, 2007, Prague, Czech Republic), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/0710.4432 | |
| dc.identifier | http://arxiv.org/abs/0710.4432 | |
| dc.identifier | SIGMA 4 (2008), 001, 9 pages | |
| dc.identifier | doi:10.3842/SIGMA.2008.001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159617 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Quantum Physics | |
| dc.subject | 46C20; 47B50; 81P10; 81R05 | |
| dc.title | On the Role of the Normalization Factors $κ_n$ and of the Pseudo-Metric ${\cal P} \neq {\cal P}^\dagger$ in Crypto-Hermitian Quantum Models | |
| dc.type | text |