Solving Mean Field Ambiguity by Flow Equations

We compare different methods used for non-perturbative calculations in strongly interacting fermionic systems. Mean field theory shows a basic ambiguity related to the possibility to perform Fierz transformations. The results depend strongly on an unphysical parameter which reflects the choice of the mean field. Renormalization group equations in a partially bosonized setting can overcome this problem if the truncation is chosen appropriately. We argue that the renormalization group approach goes beyond the lowest order Schwinger-Dyson equation and constitutes a very promising basis for the explicit treatment of condensates and spontaneous symmetry breaking.