Quantization, group contraction and zero point energy

Abstract

We study algebraic structures underlying 't Hooft's construction relating classical systems with the quantum harmonic oscillator. The role of group contraction is discussed. We propose the use of SU(1,1) for two reasons: because of the isomorphism between its representation Hilbert space and that of the harmonic oscillator and because zero point energy is implied by the representation structure. Finally, we also comment on the relation between dissipation and quantization.