ABSTRACT
This chapter analyzes the memory functions in detail. The tool is the projection operator technique introduced by R. Zwanzig and extended by H. Mori. With the help of this technique, the dispersion relations can be made into a powerful and versatile instrument as our later applications, particularly to systems of broken symmetry, should amply demonstrate. However, the projector formalism can be applied to quantum systems as well. In order not to be encumbered by incidentals, the chapter considers the formally simplest case: fluctuations of a single classical dynamical variable. It looks at the spin dynamics, to see how all of the formalism can be used. The chapter discusses the magnetization correlation function and the equilibrium-averaged autocorrelation function. The formal developments were presented for a classical system because such objects as, say, the Liouville operator are a little more familiar classically.
