Irreducibility and Compositeness in q-Deformed Harmonic Oscillator Algebras
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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.
The only modification in this replaced version is the spacing. Now the paper has 15 pages
The only modification in this replaced version is the spacing. Now the paper has 15 pages