InteractingFermions

Effective field theory and RG approach to interacting Fermions

Introduction

One of the most beautiful aspects of physics is the versatility of ideas and methods. An approach that is developed for a specific problem in a specific field may turn out to be very powerful for a completely different application. One example of such a basic, but extremely powerful tool is the idea of symmetries and in particular broken symmetries. (Broken symmetries are, in spite of their quite misleading name, perfectly valid symmetries only realized in less straightforward way than unbroken symmetries.) In this work, the method of effective field theories (EFTs) and the Renormalization group (RG), applied to interacting fermions, will be discussed. EFTs are typically associated with particle physics, the classical example being the Fermi theory of the $\beta$-decay. However, their usefulness is by far not confined to this field as will be showed in the following. This work is based mainly on the review article by R. Shankar [1] and a TASI lecture by Polchinski [2].