Multiparameter generalization of deformed particle algebras

Abstract

In this study, we generalize deformed boson and fermion algebras by considering as many deformation parameters as possible. The restriction on the number of deformation parameters emerges from the relations leaving the algebra consistent. In the bosonic part, we consider the Newton oscillator which is a one parameter generalization of the harmonic oscillator as a starting point. Then, we achieve the multiparameter generalization with d(d+1) parameters for d dimensional oscillator system. We also present the Fock representation of this oscillator. In the fermionic part, we first study the quantum group covariant two-parameter deformed fermion algebra. Then we show that if the quantum group symmetry is not preserved, then the number of deformation parameters in d dimension can be increased to 2(d-1). We study the limiting case where all deformation parameters go to zero such that the deformed fermionic oscillator reduces to the orthofermion algebra. Finally, we investigate the symmetry properties of this limiting case.