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Pseudo-Hermitian Hamiltonians and Generalized Involutory Symmetries

G. Scolarici

Czechoslovak Journal of PhysicsJan 1, 20046 citations

A non-Hermitian Hamiltonians: Pseudo 𝒫𝒯-symmetry

Mustapha Maamache, Nour El Houda Absi

International Journal of Modern Physics ASep 11, 20250 citations

Pseudo-Hermitian potential models with PT symmetry

Chun‐Sheng Jia, Shu-Chuan Li, Yun Li +1 more

Physics Letters AJul 1, 200253 citations

Pseudo-Hermitian Hamiltonians,indefinite inner product spaces and their symmetries

BLASI A, G. Scolarici, Luigi Solombrino

Jan 1, 20040 citations

Pseudo-Hermiticity and generalized PT- and CPT-symmetries

Ali Mostafazadeh

We study certain linear and antilinear symmetry generators and involution operators associated with pseudo-Hermitian Hamiltonians and show that the theory of pseudo-Hermitian operators provides a simple explanation for the recent results of Bender, Brody and Jones (quant-ph/0208076) on the CPT-symmetry of a class of PT-symmetric non-Hermitian Hamiltonians. We present a natural extension of these results to the class of diagonalizable pseudo-Hermitian Hamiltonians H with a discrete spectrum. In particular, we introduce generalized parity (𝒫), time-reversal (𝒯), and charge-conjugation (𝒞) operators and establish the 𝒫𝒯- and 𝒞𝒫𝒯-invariance of H.We study certain linear and antilinear symmetry generators and involution operators associated with pseudo-Hermitian Hamiltonians and show that the theory of pseudo-Hermitian operators provides a simple explanation for the recent results of Bender, Brody and Jones (quant-ph/0208076) on the CPT-symmetry of a class of PT-symmetric non-Hermitian Hamiltonians. We present a natural extension of these results to the class of diagonalizable pseudo-Hermitian Hamiltonians H with a discrete spectrum. In particular, we introduce generalized parity (𝒫), time-reversal (𝒯), and charge-conjugation (𝒞) operators and establish the 𝒫𝒯- and 𝒞𝒫𝒯-invariance of H.

arXiv:math-ph/0209018Journal of Mathematical PhysicsFeb 28, 2003230 citations

On the Role of the Normalization Factors κ n and of the Pseudo-Metric P ≠ P † in Crypto-Hermitian Quantum Models

Miloslav Znojil

Among P-pseudo-Hermitian Hamiltonians H = P -1 H † 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, withAmong P-pseudo-Hermitian Hamiltonians H = P -1 H † 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

arXiv:0710.4432Symmetry Integrability and Geometry Methods and ApplicationsJan 2, 200817 citations

Pseudo-Hermitian Systems, Involutive Symmetries and Pseudofermions

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