Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators

TL;DR

This paper extends the study of nonlinear pseudo-bosons and apparent non-Hermiticity to quantum models with unbounded operators, showing that the parallels from previous work persist in more complex settings.

Contribution

It demonstrates that the relationship between nonlinear pseudo-bosons and hidden non-Hermiticity remains valid in quantum models involving unbounded operators.

Findings

Parallels between pseudo-bosons and non-Hermiticity persist with unbounded operators

The framework extends to more general quantum models

Supports the robustness of the theoretical connection

Abstract

Parallels between the notions of nonlinear pseudobosons and of an apparent non-Hermiticity of observables as shown in paper I (arXiv: 1109.0605) are demonstrated to survive the transition to the quantum models based on the use of unbounded metric in the Hilbert space of states.