Three-parameter (two-sided) deformation of Heisenberg algebra

TL;DR

This paper introduces a novel three-parameter deformation of the Heisenberg algebra, revealing unique properties such as explicit particle number dependence and realizability via deformed oscillator algebra.

Contribution

It presents a new three-parameter (p,q,μ) deformation of the Heisenberg algebra with explicit N-dependence and demonstrates its realization through deformed oscillator algebra.

Findings

Deformation involves a p,q-deformed commutator and a μ-dependent term.

The μ parameter explicitly depends on the particle number operator N.

The algebra can be realized using deformed oscillator algebra.

Abstract

A 3-parametric two-sided deformation of Heisenberg algebra (HA), with p,q-deformed commutator in the l.h.s. of basic defining relation and certain deformation of its r.h.s., is introduced and studied. The third deformation parameter \mu appears in an extra term in the r.h.s. as pre-factor of Hamiltonian. For this deformation of HA we find novel properties. Namely, we prove it is possible to realize this (p,q,\mu)-deformed HA by means of some deformed oscillator algebra. Also, we find the unusual property that the deforming factor \mu\ in the considered deformed HA inevitably depends explicitly on particle number operator N. Such a novel N-dependence is special for the two-sided deformation of HA treated jointly with its deformed oscillator realizations.