Mathematics – Quantum Algebra
Scientific paper
2000-03-23
Mathematics
Quantum Algebra
The only modification in this replaced version is the spacing. Now the paper has 15 pages
Scientific paper
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.
Galetti Diogenes
Lunardi José T.
Pimentel Bruto Max
Ruzzi Maurizio
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