Self-consistent conserving theory for quantum impurity systems: Renormalization group analysis

We review the diagrammatic, conserving theory for quantum impurities with strong on-site repulsion. The method is based on auxiliary particle technique, where Wick's theorem is valid, which opens up the possibility for generalizations to more complicated situations. An analysis in terms of the perturbative renormalization group (RG) shows that on the level of the Conserving T-matrix Approximation the theory correctly describes the RG flow, including the non-scaling of potential scattering terms and the correct Kondo temperature.