ABSTRACT
This chapter discusses the quantum mechanical motion of a particle in a random potential at zero temperature. It discusses the phenomenon of Anderson localization using the developed diagrammatic technique. The central idea of the scaling theory of localization is that the conductance rather than the conductivity is the quantity of importance for determining the transport properties of a macroscopic sample. The one-parameter scaling theory of localization is based on the assumption that the dimensionless conductance solely determines the conductivity behavior of a disordered system. The phenomenon of Anderson localization can be understood in terms of the random potential acting as a mirror backscattering the electronic wave function, thereby leading to a spatial localization of the particle. In the field theoretic formulation of the localization problem, the self-consistent theory is known to be equivalent to in the effective action to keep all vacuum diagrams up to two-particle irreducible level.
