Pseudo-bosons and Riesz bi-coherent states

TL;DR

This paper introduces Riesz bi-coherent states, pairs of states sharing key features with coherent states, including resolution of the identity and eigenstate properties of pseudo-bosonic annihilation operators.

Contribution

It defines and explores Riesz bi-coherent states, extending the concept of coherent states within the pseudo-bosonic framework.

Findings

Riesz bi-coherent states produce a resolution of the identity.

They are eigenstates of two different pseudo-bosonic annihilation operators.

The states share key features with ordinary coherent states.

Abstract

After a brief review on $\D$-pseudo-bosons we introduce what we call {\em Riesz bi-coherent states}, which are pairs of states sharing with ordinary coherent states most of their features. In particular, they produce a resolution of the identity and they are eigenstates of two different annihilation operators which obey pseudo-bosonic commutation rules.