Construction of pseudo-bosons systems

TL;DR

This paper develops a general framework for pseudo-bosons using coordinate representations, extending supersymmetric quantum mechanics, and explores their connection to coherent states and modified creation-annihilation operators.

Contribution

It introduces a broad construction method for pseudo-bosons in coordinate space, expanding their theoretical foundation beyond previous models.

Findings

Extended the pseudo-bosons framework with explicit coordinate representations

Connected pseudo-bosons to coherent states and modified operators

Provided an example linking pseudo-bosons to linear operator modifications

Abstract

In a recent paper we have considered an explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. We have introduced the so-called {\em pseudo-bosons}, and the role of Riesz bases in this context has been analyzed in detail. In this paper we consider a general construction of pseudo-bosons based on an explicit {coordinate-representation}, extending what is usually done in ordinary supersymmetric quantum mechanics. We also discuss an example arising from a linear modification of standard creation and annihilation operators, and we analyze its connection with coherent states.