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arXiv · 0907.2677

Fundamental length in quantum theories with PT-symmetric Hamiltonians

Miloslav Znojil
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Abstract

The direct observability of coordinates x is often lost in PT-symmetric quantum theories. A manifestly non-local Hilbert-space metric $Θ$ enters the double-integral normalization of wave functions $ψ(x)$ there. In the context of scattering, the (necessary) return to the asymptotically fully local metric has been shown feasible, for certain family of PT-symmetric toy Hamiltonians H at least, in paper I (M. Znojil, Phys. Rev. D 78 (2008) 025026). Now we show that in a confined-motion dynamical regime the same toy model proves also suitable for an explicit control of the measure or width $θ$ of its non-locality. For this purpose each H is assigned here, constructively, the complete menu of its hermitizing metrics $Θ=Θ_θ$ distinguished by their optional "fundamental lengths" $θ\in (0,\infty)$. The local metric of paper I recurs at $θ=0$ while the most popular CPT-symmetric hermitization proves long-ranged, with $θ=\infty$.

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Miloslav Znojil. 2009-07-15. Fundamental length in quantum theories with PT-symmetric Hamiltonians. https://doi.org/10.1103/physrevd.80.045022

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