Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries

Details Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries

2002-09-10

arxiv.org/abs/math-ph/0209018v3

J.Math.Phys. 44 (2003) 974-989

Physics

Mathematical Physics

25 pages, slightly revised version, accepted for publication in J. Math. Phys

Scientific paper

10.1063/1.1539304

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 (${\cal P}$), time-reversal (${\cal T}$), and charge-conjugation (${\cal C}$) operators and establish the ${\cal PT}$- and ${\cal CPT}$-invariance of H.

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