Abstract
It is shown that the generalization of the quantum harmonic oscillator to the case of the relativistic configurational space is a q-oscillator. The corresponding group of dynamical symmetry is the quantum group SUq(1,1). The deformation parameter being q=e- omega omega 0/ where omega 0=4mc2 and omega is a frequency of the oscillator. The deformed creation and annihilation operators are finite difference ones. The corresponding deformation of the Heisenberg-Weyl group and new coherent states are also considered.