Factorized Hilbert-space metrics and non-commutative quasi-Hermitian observables

Abstract

It is well known that an (in general, non-commutative) set of non-Hermitian operators ${\Lambda }_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class of quantum models in which these operators plus the underlying physical Hilbert-space metric $\Theta$ are all represented in terms of an auxiliary operator $(N+1)-$plet $Z_k$, $k=0,1,\dots ,N$. Our formalism degenerates to the $\mathcal{P}\mathcal{T}-$symmetric quantum mechanics at $N=2$, with metric $\Theta =Z_2{Z}_1$, parity $\mathcal{P}=Z_2$, charge $\mathcal{C}=Z_1$ and Hamiltonian $H=Z_0$.

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Cited by in corpus (3)

• Systematics of quasi-Hermitian representations of non-Hermitian quantum models
• PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase
• Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation