  The question of Fermi liquid vs. non-Fermi liquid behavior induced by strong
correlations is one of the prominent problems in metallic local moment systems.
As standard models for such systems, the SU(N)xSU(M) Anderson impurity models
exhibit both Fermi liquid and non-Fermi liquid behavior, depending on their
symmetry. Taking the Anderson model as an example, these lectures first give an
introduction to the auxiliary boson method to describe correlated systems
governed by a strong, short-range electronic repulsion. It is then shown how to
include the relevant low-lying excitations (coherent spin flip and charge
fluctuation processes), while preserving the local gauge symmetry of the model.
This amounts to a conserving T-matrix approximation (CTMA). We prove a
cancellation theorem showing that the CTMA incorporates all leading and
subleading infrared singularities at any given order in a self-consistent loop
expansion of the free energy. As a result, the CTMA recovers the correct
infrared behavior of the auxiliary particle propagators, indicating that it
correctly describes both the Fermi and the non-Fermi regimes of the Anderson
model.
