  A useful tool in non perturbative studies of fermionic theories is partial
bosonization. However, partial bosonization is often connected to an ambiguity
due to Fierz rearrangement in the original theory. We discuss two different
approximations for the calculation of the effective action $\Gamma$ with
respect to a spurious dependence on the choice of Fierz transformation: Mean
field theory and the truncated flow of an exact renormalization group equation
for the effective average action.
