the flow. A first proposal, how this can be realized with help of a scale-dependent nonlinear field transformation was formulated in ref. [@GiesWetterich] and used to study bound state formation in the NJL model. The analysis in the present paper is based on a recently derived, simple, but nevertheless exact flow equation [@FW09]. Although the spirit is similar to the formalism proposed in ref. [@GiesWetterich], there are some differences in the implementation.

This paper is organized as follows. In chapter \[sec:nonrelativisticmodel\] we introduce our notation and the microscopic model for nonrelativistic particles with an instantaneous interaction. In the subsequent section \[sec:Partialbosonization\] we show how this model can be treated using partial bosonization and an exact flow equation where the Hubbard-Stratonovich transformation is kept fixed, i.e. independent of the renormalization scale $k$. In this approach we can integrate the flow equation exactly. However, this solution relies on some particular features of the nonrelativistic theory and is difficult to generalize to more complicated cases. Therefore we discuss an alternative approach to the problem in section \[sec:scaledeppartialbos\]. Here we work with a scale-dependent Hubbard-Stratonovich transformation. Again, it is possible to integrate the resulting flow equations exactly in the nonrelativistic case. We argue at 