Quasibosons composed of two q-fermions: realization by deformed oscillators

TL;DR

This paper constructs a mathematical realization of quasibosons, composite particles made of two fermions or q-fermions, using deformed oscillators, revealing unique deformation structures and their properties.

Contribution

It explicitly derives the deformation structure function for quasibosons composed of two fermions or q-fermions, establishing a unique realization via deformed oscillators.

Findings

Realization achieved with quadratic polynomial DSF for two fermions.

For q-fermions, DSF includes q parameter and does not smoothly converge to the fermion case.

Provides explicit restrictions and structure functions for quasiboson operator algebra.

Abstract

Composite bosons, here called {\it quasibosons} (e.g. mesons, excitons, etc.), occur in various physical situations. Quasibosons differ from bosons or fermions as their creation and annihilation operators obey non-standard commutation relations, even for the "fermion+fermion" composites. Our aim is to realize the operator algebra of quasibosons composed of two fermions or two q-fermions (q-deformed fermions) by the respective operators of deformed oscillators, the widely studied objects. For this, the restrictions on quasiboson creation/annihilation operators and on the deformed oscillator (deformed boson) algebra are obtained. Their resolving proves uniqueness of the family of deformations and gives explicitly the deformation structure function (DSF) which provides the desired realization. In case of two fermions as constituents, such realization is achieved when the DSF is quadratic polynomial in the number operator. In the case of two q-fermions, q\neq 1, the obtained DSF inherits the parameter q and does not continuously converge when q\to 1 to the DSF of the first case.