Abstract
We propose definitions of generalized parity (P), time-reversal (T) and charge-conjugation (C) operators such, that any diagonalizable pseudo-Hermitian Hamiltonian is invariant under the involutory symmetries C, TP, and CPT. We inquire about the peculiarities of such symmetries showing that these constitute the P-unitary and P-antiunitary symmetry generators. Moreover, we give a necessary and sufficient condition for diagonalizable pseudo-Hermitian Hamiltonians to admit P-pseudounitary and P-pseudoantiunitary symmetries.
Similar content being viewed by others
References
C.M. Bender, D.C. Brody, and H.F. Jones: Phys. Rev. Lett. 89 (2002) 270401.
A. Mostafazadeh: J. Math. Phys. 44 (2003) 974.
L. Bracci, G. Morchio, and F. Strocchi: Commun. Math. Phys. 41 (1975) 289.
A. Blasi, G. Scolarici, and L. Solombrino: Pseudo-Hermitian Hamiltonians, indefinite inner products spaces and their symmetries (in preparation).
A. Mostafazadeh: J. Math. Phys. 43 (2002) 3944.
L. Solombrino: J. Math. Phys. 43 (2002) 5439.
G. Scolarici and L. Solombrino: J. Math. Phys. 44 (2003) 4450.
St. Weigert: J. Opt. B 5 (2003) S416.
C.M. Bender, P.N. Meisinger, and Q. Wang: J. Phys. A 36 (2003) 6791.
A. Mostafazadeh: Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics, math-ph/0302050 (2003).
G. Scolarici and L. Solombrino: Phys. Lett. A 303 (2002) 239.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Scolarici, G. Pseudo-Hermitian Hamiltonians and Generalized Involutory Symmetries. Czechoslovak Journal of Physics 54, 119–127 (2004). https://doi.org/10.1023/B:CJOP.0000014376.17004.d6
Issue Date:
DOI: https://doi.org/10.1023/B:CJOP.0000014376.17004.d6