formation of bound states. As a simple example and to develop the formalism, we consider well known problem of nonrelativistic particles with instantaneous interaction. In this case we can solve the flow equations exactly and we show that our formalism is equivalent to the standard quantum mechanical description although it is based on a field theoretic approach.

In principle, since the flow equation is exact, it can describe also more complicated situations for example with relativistic particles, retarded interactions or at nonzero density. However, one cannot expect to find exact solutions to the flow equations, there. The merit of our formalism is to provide a convenient starting point for approximations. These do not have to rely on the existence of a small coupling constant as in usual perturbation theory and have the potential to capture nonperturbative effects. We discuss a generic scheme for the construction of such approximations. The resulting formalism is quite general and can be seen as a method to resolve the momentum dependence of vertices in renormalization group flow equations.

We mention that flow equations for bound states have been investigated previously. A setup based on Wegner’s flow equation for Hamiltonians [@Wegner] and the similarity renormalization group 