that no solution in a closed form can be expected.

Although one cannot expect to find analytic solutions by transferring the above calculation to a relativistic field theory, one might ask whether it can be helpful for finding approximate solutions. One could make a truncation of the flowing action $\Gamma_k$ for example in terms of a derivative expansion and consider the flow equations in the theory-subspace spanned by the finite number of operators included in this truncation. Indeed, we will argue below that such truncations can lead to good approximate solutions. The formulation in the present section has one drawback for approximate solutions, however. As already discussed above, interactions in relatvistic field theories are usually mediated by exchange fields such as the photon. The renormalization of the corresponding couplings and propagators can be calculated most efficient in a formulation of the theory which directly takes the exchange fields as propagating fields into account. Other formulations where these fields (as for example the photon) are “integrated out” might be equivalent in principle, but are usually much harder to treat by approximate methods. The reason is that the essential momentum- and frequency dependence is often hidden in such formulations.

Transfered to the 