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Effective field theories

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.