The Renormalization group in non-relativistic theories

Abstract

The resummation of logarithms in Quantum Field Theories is a long tale plenty of successes, yet the resummation of logarithms in non-relativistic theories has remained elusive. This was the most frustrating, since the first quantum field theory log ever computed was the Lamb shift one. We briefly review recent progress on the resummation of logarithms of $\alpha$, which appear in the physics of non-relativistic states, using effective field theories. We put special emphasis on the basic formalism.