SUQ(1, 1) AND THE RELATIVISTIC OSCILLATOR

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 SU(q)(1, 1). The deformation parameter being q = e-omega/omega-0 where hBAR-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.