Generalized Heisenberg algebra and (non linear) pseudo-bosons

TL;DR

This paper introduces a deformed generalized Heisenberg algebra using pseudo-boson techniques, relevant for non self-adjoint Hamiltonians, and explores connections with nonlinear pseudo-bosons through various examples.

Contribution

It presents a novel deformation of the generalized Heisenberg algebra incorporating pseudo-boson methods, extending the framework to non-Hermitian quantum systems.

Findings

Development of a deformed algebra framework

Application to non self-adjoint Hamiltonians

Illustrative examples demonstrating the theory

Abstract

We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint Hamiltonians are needed to describe a given physical system. We also discuss relations with nonlinear pseudo-bosons. Several examples are discussed.