Eq.  we performed a Hubbard-Stratonovich transformation and introduced the bilocal field $\Phi$. In this “partially bosonized” language it was possible to find a solution of the flow equation for the propagator of the field $\Phi$ in a closed form. Note however, that this solution relies on some features particular to the nonrelativistic few-body problem. First, the description of the interaction between particles in terms of a instantaneous interaction potential $V(\vec x_1-\vec x_2)$ is usually not possible for relativistic problems. In relativistic quantum field theory, interactions are mediated by exchange particles such as the photon. In momentum space the resulting interaction term has nontrivial frequency- and momentum dependence and is subject to renormalization group modifications for example due to a “running” fine-structure constant $\alpha$ or charge $e$. These features make it difficult to absorb the interaction term by an appropriate Hubbard-Stratonovich transformation. Even if this was possible, solving the flow equations would be more difficult than in the nonrelativistic case presented above. Both the propagator for the field $\psi$ and the Yukawa interaction $\sim \Phi^* \psi_1\psi_2+c.c.$ might have non-vanishing flow equations. These equations as well as the flow equations for the propagator of $\Phi$ would depend on higher-order vertex functions such 