ABSTRACT
This chapter considers the interaction between a single degree of freedom and an environment. It assumes that the environment can be represented by a set of harmonic oscillators, and that the interaction between the system of interest and the environment is linear in the coupling to the oscillator degrees of freedom. There are systems where the linear coupling to the environment degrees of freedom is exact, such as the fundamental interaction of a charged particle interacting with the electromagnetic field, electron-photon interaction. Furthermore, many situations are adequately described by such an interaction, because it is sufficient to consider each environment degree of freedom only weakly perturbed. The chapter examines the time evolution of the reduced density matrix on integral form, and described the diagrammatic expansion in the spatial representation. It explores the kinetic approach for studying the motion of a particle interacting with an oscillator environment.
