  Starting from the basic path integral in phase space we reconsider the
functional approach to the RG flow of the one particle irreducible effective
average action. On employing a balanced coarse-graining procedure for the
canonical variables we obtain a functional integral with a non trivial measure
which leads to a modified flow equation. We first address quantum mechanics for
boson and fermion degrees of freedom and we then extend the construction to
quantum field theories. For this modified flow equation we discuss the
reconstruction of the bare action and the implications on the computation of
the vacuum energy density.
