Abstract
The current applications of non-Hermitian but PT-symmetric Hamiltonians H cover several, mutually not too closely connected subdomains of quantum physics. Mathematically, the split between the open and closed systems can be characterized by the respective triviality and non-triviality of an auxiliary inner-product metric Θ=Θ(H). With our attention restricted to the latter, mathematically more interesting unitary-evolution case we show that the intuitive but technically decisive simplification of the theory achieved via an “additional” PCT-symmetry constraint upon H can be given a deeper mathematical meaning via introduction of a certain second auxiliary inner product.
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