Quantum mechanics using two auxiliary inner products

DOI10.1016/J.PHYSLETA.2021.127792arXiv2110.12155MaRDI QIDQ6381088

Miloslav Znojil

Publication date: 23 October 2021

Abstract: The current applications of non-Hermitian but $calPT-$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 $Theta=Theta(H)$. 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" $calPCT-$symmetry constraint upon $H$ can be given a deeper mathematical meaning via introduction of a certain second auxiliary inner product.

Mathematics Subject Classification ID

Quantum theory (81-XX) Statistical mechanics, structure of matter (82-XX)

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