Functional-integral approach to the Anderson model for dilute magnetic alloys from the viewpoint of diagrammatic perturbation technique

The grand partition function for the Anderson model can be expressed as a Gaussian average over the partition function of a one-particle system in a fluctuating external potential. Though the zero-frequency approximation for this potential leads to the correct well-known two limits of the Anderson model, it turns out to be insufficient even for the first corrections to these limits. Combining diagrammatic techniques and the functional-integral approach, we use a new kind of perturbation theory in order to find approximations which fulfill the requirement of giving the first few corrections to both limits. They correspond to approximations in the functional integral, which take into account an infinite number of non-Gaussian fluctuations around the static frequency of the external field, and which thus are inaccessible by the usual treatment. In particular, the Kondo effect is shown to result from singularities in the particle-hole propagation. The analysis of the paper suggests that the use of one random field in the functional-integral approach leads to greater technical difficulties than encountered in other comparable many-body methods.