The scattering of fast particles is an important tool in many fields of physics. In particular, virtually all that is known about elementary particles is a result of the interpretation of scattering experiments. In condensed matter physics as well, the bulk of our understanding of materials on a microscopic level comes from the scattering of neutrons, photons and electrons. Neutrons are used to determine crystal structures and to probe the dynamical properties of solids; photons are used in a plethora of spectroscopies to elucidate the details of the electronic and magnetic structure. Some of these will be discussed in chapter 12. Electrons can be used to determine the behaviour of surface plasmons and also to look at electronic transitions.

For these and many other reasons, an understanding of the quantum theory of scattering is of key importance for a theoretical physicist. Therefore in this chapter we develop relativistic scattering theory from scratch. This chapter doesn't assume any knowledge of non-relativistic scattering theory although such knowledge will aid your understanding.

In this chapter it has been necessary to include some mathematical preliminaries. Therefore the first three sections are an introduction to Green's functions and their uses. Later in the chapter we have some followup sections on free-particle and scattering Green's functions.