introduce an additional functional integral over a bilocal composite fields $\Phi(x,\vec y)$ where $\vec y$ labels the relative coordinate of the two particles. For more complicated problems it is difficult to follow the RG flow for bilocal fields. It is therefore necessary to find useful approximation schemes. One possibility is to expand the field in terms of an complete orthonormal set of functions $f_n(\vec y)$ like $$\Phi(x,\vec y) = \sum_{n\in {\cal I}} \phi_n(x) f_n(\vec y).$$ One can then consider the flow of the propagator and coupling constants in that basis. A sensible approximation would now be to take only a finite subset ${\cal J}$ of the infinite index set ${\cal I}$ into account and to neglect all couplings between the fields $\phi_n$, $n\in {\cal J}$ and the fields $\phi_n$, $n\notin {\cal J}$. The approximation becomes good if the influence of the neglected couplings onto the flow of the considered quantities is small. This will, of course, only work for some particular choices of the set $f_n(\vec y)$.

In the following we will consider as an example a Yukawa potential of the form $$V(\vec x-\vec y) = \frac{-e^2}{4\pi |\vec x_1-\vec x_2|} e^{-m|\vec x_1-\vec x_2|}.
\label{eq:Yukawapot}$$ Note that for $m\to \infty$ this 