Quadratic algebras :Three-mode bosonic realizations and applications

TL;DR

This paper explores quadratic algebras using three-mode bosonic realizations, providing matrix and differential operator representations, and discusses their physical applications.

Contribution

It introduces new three-mode bosonic realizations of quadratic algebras and demonstrates their matrix and differential operator representations.

Findings

Derived matrix representations of quadratic algebras.

Constructed single variable differential operator realizations.

Presented physical examples illustrating the relevance of these algebras.

Abstract

Quadratic algebras of the type $\lsb Q_0, Q_\pm \rsb$ $=$ $\pm Q_\pm$, $\lsb Q_+, Q_- \rsb$ $=$ $aQ_0^2 + bQ_0 + c$ are studied using three-mode bosonic realizations. Matrix representations and single variable differential operator realizations are obtained. Examples of physical relevance of such algebras are given.