Related papers: Quantum mechanics using two auxiliary inner products

Quantum mechanics using two auxiliary inner products

URL: http://arxiv.org/abs/2110.12155v1
Date: Sat, 23 Oct 2021 06:47:35 GMT
Title: Quantum mechanics using two auxiliary inner products
Authors: Miloslav Znojil
Abstract summary: We show that the intuitive but technically decisive simplification of the theory achieved via an "additional" $cal PCT-$symmetry constraint upon $H$ can be given a deeper mathematical meaning.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: The current applications of non-Hermitian but ${\cal PT}-$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 $\Theta=\Theta(H)$. 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" ${\cal PCT}-$symmetry constraint upon $H$ can be given a deeper mathematical meaning via introduction of a certain second auxiliary inner product.

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