Quantum mechanics using two auxiliary inner products

Abstract

The current applications of non-Hermitian but $\mathcal{P}\mathcal{T}-$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" $\mathcal{P}\mathcal{C}\mathcal{T}-$symmetry constraint upon $H$ can be given a deeper mathematical meaning via introduction of a certain second auxiliary inner product.

arXiv comment16 pp

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Cited by in corpus (2)

• Dyson Maps and Unitary Evolution for Maxwell Equations in Tensor Dielectric Media
• Systematics of quasi-Hermitian representations of non-Hermitian quantum models