Fundamental length in quantum theories with PT-symmetric Hamiltonians

Details Fundamental length in quantum theories with PT-symmetric Hamiltonians Fundamental length in quantum theories with PT-symmetric Hamiltonians

2009-07-15

arxiv.org/abs/0907.2677v1

Phys.Rev.D80:045022,2009

Physics

High Energy Physics

High Energy Physics - Theory

31 pp, 3 figures

Scientific paper

10.1103/PhysRevD.80.045022

The direct observability of coordinates x is often lost in PT-symmetric quantum theories. A manifestly non-local Hilbert-space metric $\Theta$ enters the double-integral normalization of wave functions $\psi(x)$ 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 $\theta$ of its non-locality. For this purpose each H is assigned here, constructively, the complete menu of its hermitizing metrics $\Theta=\Theta_\theta$ distinguished by their optional "fundamental lengths" $\theta\in (0,\infty)$. The local metric of paper I recurs at $\theta=0$ while the most popular CPT-symmetric hermitization proves long-ranged, with $\theta=\infty$.

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