Fermi and non-Fermi Liquid Behavior in Quantum Impurity Systems: Conserving Auxiliary Particle Theory

We review a recently developed method, based on an exact auxiliary boson representation, to describe both Fermi liquid and non-Fermi liquid behavior in quantum impurity systems. Coherent spin and charge fluctuation processes are taken into account in a self-consistent way and are shown to include {\it all} leading and subleading infrared singularities at any given order of the self-consistent loop expansion of the free energy. As a consequence, for the SU(N)$\times$ SU(M) Anderson impurity models the correct temperature dependence of the susceptibility is recovered over the entire temperature range, including Fermi liquid or non-Fermi liquid behavior below the Kondo temperature $T_K$. As a standard diagram technique the presented method has the potential to be generalized to correlated electron systems on a lattice.