Generalized q-Oscillators and their Hopf Structures

TL;DR

This paper explores various forms of the q-oscillator algebra, investigates conditions for Hopf structures, and introduces a generalized algebra with multimode extensions, advancing the mathematical framework of quantum oscillators.

Contribution

It introduces a generalized q-oscillator algebra with Hopf structures and multimode extensions, expanding the theoretical understanding of quantum algebra frameworks.

Findings

Identified conditions for Hopf structures in q-oscillator algebras

Proposed a new generalized q-oscillator algebra

Extended the algebra to multimode systems

Abstract

We study the relationships among the various forms of the $q$ oscillator algebra and consider the conditions under which it supports a Hopf structure. We also present a generalization of this algebra together with its corresponding Hopf structure. Its multimode extensions are also considered.