DYNAMIC NONLINEAR SIGMA-MODEL OF LOCALIZATION THEORY

The noninteracting disordered electron system is studied in the framework of a real-time, finite-temperature quantum field theory, the so-called time-path formalism. This formalism enables us to perform an initial-stage disorder averaging without the use of replicas or superfields, leading to an effective action from which disorder averaged quantities can be calculated directly. A "dynamic" nonlinear σ model for a matrix field is derived as an effective theory for the diffusion modes. The matrix field depends on two energy arguments, the external frequency and the characteristic energy scale of interest. These energy arguments play a role similar to the replica or superfield indices. The averaging methods are compared on a perturbative level both in the impurity- and the diffusion-diagram techniques. The loop-contributions, which arise as a consequence of the initial-stage disorder averaging, vanish due to the matrix structure of the diffusion mode. The renormalization of the dynamic nonlinear σ model is shown to lead to the same result as the replica and superfield models. © 1990.