  We develop a new analytical method for solving real time evolution problems
of quantum many-body systems. Our approach is a direct generalization of the
well-known canonical perturbation theory for classical systems. Similar to
canonical perturbation theory, secular terms are avoided in a systematic
expansion and one obtains stable long-time behavior. These general ideas are
illustrated by applying them to the spin-boson model and studying its
non-equilibrium spin dynamics.
