**Effective Field Theory lectures at the Winter School at Perimeter Institute (Jan/Feb 2023):**

The overall plan of these notes is to start with a familiar theory – QED – in order to illustrate many of the basic principles of EFT. Then we consider a more complex theory – the non-linear sigma model – to show how EFT must be a full QFT. This is followed a discussion of some useful techniques. We end with the EFT treatment of quantum General Relativity.

Preliminary comments Lecture 1 QED and measurements. The effect of a heavy fermion. An effective Lagrangian. Counting of dimenstions. Ingredients to the radiative correction. Locality and the Appelquist Carazzone theorem. Why do quantum calculations work? The energy expansion. Matching or measuring. Start of Path Integral language. Link to the video

Lecture 2 Path Integrals – “integrating out.” EFT 1.0 – Effective Lagrangians for new physics. EFT is a full QFT. The linear sigma model. Constructing the nonlinear sigma model. Haag’s theorem and reparameterization invariance. Loops. The general Effective Lagrangian and power counting. Matching at one-loop level. Start of the Background Field Method – QED again. Link to the video

Lecture 3 Generalization of background field method. Renormalization of the nonlinear sigma model. The QCD story – comparison with experiment. The Operator Product Expansion – matching and running between scales. Link to the video

Lecture 4 Quantum General Relativity as an EFT. Reminder – gauge theory form symmetry. General Relativity from Symmetry and Noether’s Theorem. The EFT treatment of GR. Background Field expansion and renormalization. A calculation. Thinking like an effective field theorist. Lessons from the gravitational potential. Bending of light and implications. Limits of the EFT. Link to the video