SUQ,H-]0(2) AND SUQ,H(2), THE CLASSICAL AND QUANTUM Q-DEFORMATIONS OF THE SU(2) ALGEBRA

By means of classical harmonic oscillators and their canonical quantization, we show that the q-deformation of the SU(2) Lie algebra can be realized at a classical level in the sense of Poisson brackets, denoted by SUq,(inf) not=0(2), and that the canonical quantization of the system leads to the quantum q-deformation of the SU(2) algebra, denoted by SU q,(2). This means that the q-deformation and the h(cross)- quantization are in general two different concepts.