Quons, coherent states and intertwining operators

TL;DR

This paper develops a differential operator representation for q-mutation relations, constructs associated coherent states, and creates nearly isospectral quonic Hamiltonians using intertwining operators.

Contribution

It introduces a generalized differential representation for q-mutation operators, constructs new coherent states, and develops methods for generating almost isospectral quonic Hamiltonians.

Findings

Differential representation for q-mutation operators generalized.

Construction of non-linear and Gazeau-Klauder coherent states.

Development of almost isospectral quonic Hamiltonians.

Abstract

We propose a differential representation for the operators satisfying the q-mutation relation $BB^\dagger-q B^\dagger B=\1$ which generalizes a recent result by Eremin and Meldianov, and we discuss in detail this choice in the limit $q\to1$. Further, we build up non-linear and Gazeau-Klauder coherent states associated to the free quonic hamiltonian $h_1=B^\dagger B$. Finally we construct almost isospectrals quonic hamiltonians adopting the results on intertwining operators recently proposed by the author.