Few-body physics with functional renormalization

Abstract

In this thesis nonrelativistic few-body quantum physics is investigated with the method of functional renormalization. In particular, we discuss different theoretical aspects of few-body physics related to the Efimov effect. Our central finding is that this effect manifests itself as a renormalization group limit cycle. First, we treat the problem of a singular, inverse square potential in quantum mechanics. Then we examine the original Efimov problem of three particles interacting via a short-range two-body potential. Subsequently, we present a first step towards the renormalization group solution of the four-body quantum problem for bosons. Finally, a general theoretical feature of the Efimov physics, composite operators with complex scaling dimensions, are discussed.