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Pseudo-Hermiticity and generalized \(PT\)- and \(CPT\)-symmetries. (English) Zbl 1061.81076

Summary: 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 C. M. Bender, D. C. Brody and H. F. Jones [Phys. Rev. Lett. 89, No. 27, 270401 (2002), see also 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 \(H\).

MSC:

81U15 Exactly and quasi-solvable systems arising in quantum theory
47N50 Applications of operator theory in the physical sciences
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References:

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