Effective field theories

TL;DR

This paper provides a pedagogical overview of low-energy effective field theories, illustrating how heavy particles are integrated out in QED and QCD, and introduces the method of regions as an alternative approach.

Contribution

It offers a clear, educational introduction to effective field theories with detailed QED examples and a brief discussion of QCD applications and the method of regions.

Findings

Effective field theories simplify low-energy physics calculations.

Heavy particles can be integrated out to derive effective theories.

The method of regions offers an alternative perspective on low-energy limits.

Abstract

A pedagogical introduction to low-energy effective field theories. In some of them, heavy particles are "integrated out" (a typical example - the Heisenberg-Euler EFT); in some heavy particles remain but some of their degrees of freedom are "integrated out" (Bloch-Nordsieck EFT). A large part of these lectures is, technically, in the framework of QED. QCD examples, namely, decoupling of heavy flavors and HQET, are discussed only briefly. However, effective field theories of QCD are very similar to the QED case, there are just some small technical complications: more diagrams, color factors, etc. The method of regions provides an alternative view at low-energy effective theories; it is also briefly introduced.