Two-fermion composite quasi-bosons and deformed oscillators

TL;DR

This paper demonstrates that deformed oscillators can be consistently used to realize quasi-boson operators, which are composite particles made of two fermions, and establishes conditions and uniqueness for such realizations.

Contribution

It proves the existence and uniqueness of deformed oscillators that can represent quasi-boson operators composed of two fermions.

Findings

Deformed oscillators can realize quasi-boson operators.

Conditions for consistent realization are derived.

The family of deformations is shown to be unique.

Abstract

The concept of quasi-bosons or composite bosons (like mesons, excitons etc.) has a wide range of potential physical applications. Even composed of two pure fermions, the quasi-boson creation and annihilation operators satisfy non-standard commutation relations. It is natural to try to realize the quasi-boson operators by the operators of deformed (nonlinear) oscillator, the latter constituting widely studied field of modern quantum physics. In this paper, it is proved that the deformed oscillators which realize quasi-boson operators in a consistent way really exist. The conditions for such realization are derived, and the uniqueness of the family of deformations under consideration is shown.