2000/03/23 by D. Galetti, J. T. Lunardi, Galetti, D. +6
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP #math.QA
paper · pdf · doi:10.48550/arxiv.math/0003143
The only modification in this replaced version is the spacing. Now the paper has 15 pages
openalex publication_date 2000/03/23 · arxiv created 2000/03/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
q-Deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is discussed by using an extension of the number concept proposed by Gauss, namely the Q-numbers. A study of the reducibility of the Fock space representation which explores the properties of the Gauss polynomials is presented. When the deformation parameter is a root of unity, an interesting result comes out in the form of a reducibility scheme for the space representation which is based on the classification of the primitive or non-primitive character of the deformation parameter. An application is carried out for a q-deformed harmonic oscillator Hamiltonian, to which the reducibility scheme is explicitly applied. For finite-dimensional spaces associated to non-primitive roots of unity the compositeness of the k-fermions/quons is discussed.