Pseudo-bosons, Riesz bases and coherent states

TL;DR

This paper revisits a PT-symmetric quantum model, emphasizing the importance of Riesz bases and providing a rigorous mathematical analysis of the associated coherent states.

Contribution

It offers a detailed, mathematically rigorous extension of Trifonov's PT-symmetric model, highlighting the role of Riesz bases and constructing coherent states.

Findings

Riesz bases are crucial for the model's mathematical consistency

The paper clarifies the formal aspects of the PT-symmetric system

Coherent states associated with the model are explicitly constructed

Abstract

In a recent paper, Trifonov suggested a possible explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. Although being rather intriguing, in his treatment many mathematical aspects of the model have just been neglected, making most of the results of that paper purely formal. For this reason we are re-considering the same model and we repeat and extend the same construction paying particular attention to all the subtle mathematical points. From our analysis the crucial role of Riesz bases clearly emerges. We also consider coherent states associated to the model.