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Two-Parameter Deformed SUSY Algebra for Fibonacci Oscillators

Authors:	Abdullah Algin Metin Arik Deniz Kocabicakoglu

Institution:	(1) Department of Physics, Faculty of Arts and Sciences, Eskisehir Osmangazi University, Meselik, 26480 Eskisehir, Turkey;(2) Department of Physics, Faculty of Arts and Sciences, Bogazici University, Bebek, Istanbul, Turkey;(3) Graduate School of Sciences, Eskisehir Osmangazi University, Meselik, 26480 Eskisehir, Turkey

Abstract:	We construct a two-parameter deformed SUSY algebra for the system of n ordinary fermions and n(q ₁,q ₂)-deformed bosons called Fibonacci oscillators with $\mathit{SU}_{q_{1}/q_{2}}(n)$ -symmetry. We then analyze the Fock space representation of the algebra constructed. We obtain the total deformed Hamiltonian and the energy levels together with their degeneracies for the system. We also consider some physical applications of the Fibonacci oscillators with $\mathit{SU}_{q_{1}/q_{2}}(n)$ -symmetry, and discuss the main reasons to consider two distinct deformation parameters.

Keywords:	Deformed bosons Quantum groups Quantum superalgebras
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