  During the last few years, investigations of Rare-Earth materials have made
clear that not only the heavy fermion phase in these systems provides
interesting physics, but the quantum criticality where such a phase dies
exhibits novel phase transition physics not fully understood. Moreover,
attempts to study the critical point numerically face the infamous fermion sign
problem, which limits their accuracy. Effective action techniques and
Callan-Symanzik equations have been very popular in high energy physics, where
they enjoy a good record of success. Yet, they have been little exploited for
fermionic systems in condensed matter physics. In this work, we apply the RG
effective action and Callan-Symanzik techiques to the heavy fermion problem. We
write for the first time the effective action describing the low energy physics
of the system. The f-fermions are replaced by a dynamical scalar field whose
nonzero expected value corresponds to the heavy fermion phase. This removes the
fermion sign problem, making the effective action amenable to numerical studies
as the effective theory is bosonic. Renormalization group studies of the
effective action can be performed to extract approximations to nonperturbative
effects at the transition. By performing one-loop renormalizations, resummed
via Callan-Symanzik methods, we describe the heavy fermion criticality and
predict the heavy fermion critical dynamical susceptibility and critical
specific heat. The specific heat coefficient exponent we obtain (0.39) is in
excellent agreement with the experimental result at low temperatures (0.4).
