A unified representation of the q-oscillator and the q-plane

TL;DR

This paper introduces a unified algebraic framework that deforms position and momentum operators, connecting the q-oscillator and q-plane structures through relativistic-inspired deformations.

Contribution

It presents a novel algebraic deformation that unifies the q-oscillator and q-plane, bridging two important quantum algebraic structures.

Findings

The algebra reduces to the q-oscillator in a specific limit.

The algebra reproduces the q-plane commutation relation in another limit.

Deformations are motivated by relativistic and phase space symmetries.

Abstract

Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and the q-plane commutation relation in another.