Many-Body Perturbation Theory

This chapter deals with the field theoretical method to many-body systems, especially the path-integral formalism for fermions with use of Grassmann numbers. Green function appears as a natural element in Feynman diagram that represents a group of terms in many-body perturbation theory. The graphical method appeals to intuition, and is convenient to reorganize the perturbation series to infinite order. The discussion in this chapter is rather technical, but is most useful in understanding physical concepts including the dynamical mean field theory to be explained in the next chapter.