QUANTUM DISSIPATION AND QUANTUM GROUPS

We discuss the role of quantum deformation of Weyl-Heisenberg algebra in dissipative systems and finite temperature systems. We express the time evolution generator of the damped harmonic oscillator and the gen erator of thermal Bogolubov transformations in terms of operators of t he quantum Weyl-Heisenberg algebra. The quantum parameter acts as a la bel for the unitarily inequivalent representations of the canonical co mmutation relations in which the space of the states splits in the inf inite volume limit. (C) Academic Press, Inc.