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

A. Blasi·G. Scolarici·L. Solombrino
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Abstract

We extend the definition of generalized parity $P$, charge-conjugation $C$ and time-reversal $T$ operators to nondiagonalizable pseudo-Hermitian Hamiltonians, and we use these generalized operators to describe the full set of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold classification. In particular we show that $TP$ and $CTP$ are the generators of the antiunitary symmetries; moreover, a necessary and sufficient condition is provided for a pseudo-Hermitian Hamiltonian $H$ to admit a $P$-reflecting symmetry which generates the $P$-pseudounitary and the $P$-pseudoantiunitary symmetries. Finally, a physical example is considered and some hints on the $P$-unitary evolution of a physical system are also given.

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A. Blasi, G. Scolarici, L. Solombrino. 2004-02-27. Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries. https://doi.org/10.1088/0305-4470/37/15/003

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