The kappa-deformed boson algebra and parafermion algebra

Abstract

In this paper we consider kappa-deformed boson algebra [a, a(dagger)] = 1 + 2 kappa N. We discuss the kappa-deformed quantum harmonic oscillator problem. We also apply this algebra to the photon and phonon to formulate the kappa-deformed Planck radiation law and kappa-deformed Debye model and compare our results with undeformed ones. Finally, we discuss the case of kappa = -1/p which gives the parafermion model.