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Europhysics Letters (EPL)

Uniqueness of Boson Realization of Fermions

Bijan Kumar Bagchi

Published Aug 1, 1994• 2 citations
Publisher

Abstract

The question of boson realization of fermions is considered in the general context of q -deformation.
DOI
10.1209/0295-5075/27/4/013

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Composite bosons, here called 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 the uniqueness of the family of deformations and gives explicitly the deformation structure function (DSF) which provides the desired realization. In the case of two fermions as constituents, such realization is achieved when the DSF is a quadratic polynomial in the number operator. In the case of two q -fermions, q ≠ 1, the obtained DSF inherits the parameter q and does not continuously converge when q → 1 to the DSF of the first case.
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.