In this lecture, we review the experimental situation of heavy Fermions with
emphasis on the existence of a quantum phase transition (QPT) and related
non-Fermi liquid (NFL) effects. We overview the Kondo lattice model (KLM) which
is believed to describe the physics of those systems. After recalling the
existing theories based on large-N expansion and various N=2 schemes, we
present two alternative approaches: (i) a spin fluctuation-Kondo functional
integral approach treating the spin-fluctuation and Kondo effects on an equal
footing, and (ii) a supersymmetric theory enlarging the usual fermionic
representation of the spin into a mixed fermionic-bosonic representation in
order to describe the spin degrees of freedom as well as the Fermi-liquid type
excitations. This kind of approaches may open up new prospects for the
description of the critical phenomena associated to the quantum phase
transition in Heavy-Fermion systems.Comment: 27 pages, 6 figures, 51 references, appeared in the Proceedings of
the XXXVIII Cracow School of Theoretical Physics, Zakopane, Poland, June
1-10, 199