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abstract: 'We develop a formalism to describe the formation of bound states in quantum field theory using an exact renormalization group flow equation. As a concrete example we investigate a nonrelativistic field theory with instantaneous interaction where the flow equations can be solved exactly. However, the formalism is more general and can be applied to relativistic field theories, as well. We also discuss expansion schemes that can be used to find approximate solutions of the flow equations including the essential momentum dependence.'
author:
- 'S. Floerchinger'
title: Exact flow equation for bound states
---

Introduction
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The formation of bound states was one of the first problems discussed in quantum mechanics. Although the quantum mechanical formalism for nonrelativistic particles with instantaneous interaction is simple and easy to apply, it is much more difficult to treat the problem in quantum field theory as needed for example for relativistic particles. The Bethe-Salpeter [@BetheSalpeter] equation can be used to sum Ladder diagrams but it is difficult to go beyond [@Weinberg]. For that reason it is sensible to look for alternative approaches.

In this paper we show how a recently derived exact renormalization group flow equation [@FW09] can be used to treat the 