ABSTRACT
This chapter considers the impurity-averaged current and density responses. It focuses on the diagrammatic technique and develops the diagrammatic method directly for the correlation functions which describe the linear response of a system. The chapter establishes what the Boltzmann conductivity amounts to in terms of conductivity diagrams, and describes the diffusion propagator in terms of diagrams. The impurity-averaged density response is, to linear order in the applied potential, described by the impurity average of the product of two propagators. The typical structure of the impurity-averaged response function is the impurity average of a product of propagators. The topological character of the definition of various irreducible sets of diagrams leads to certain interrelations between them, and expresses in diagrammatic terms the conservation laws obeyed by the system. The chapter explores the consequence of particle conservation, establishing a relation between the self-energy and the irreducible four-point vertex.
