2011/07/31 by A. M. Gavrilik, A M Gavrilik, I. I. Kachurik +3 · 2 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Boson #Creation and annihilation operators #Deformation (meteorology) #Fermion #Operator (biology) #Quadratic equation #Quantum Mechanics and Non-Hermitian Physics #Realization (probability) #cond-mat.other #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/44/47/475303
published as J. Phys. A: Math. Theor., vol.44 (2011) 475303 · 24 pages; v2: new appendix with particular examples given, few references added, minor textual changes made
openalex publication_date 2011/11/03 · arxiv created 2011/11/10 · arxiv updated 2011/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.