Effective Field Theory

These lectures were given at the MITP Summer School 2018: Towards the Next Effective Quantum Field Theory of Nature. They provide a first introduction to effective field theory, illustrating the basic concepts with concrete examples, mostly from QED.

Lecture 1: Introduction (notes, video)

  1. Basic terminology, steps in the construction of an effective theory

  2. Operator dimension

  3. Why effective theories?

Lecture 2: Construction of Leff (notes, video)

  1. QED at very low energy: the Euler-Heisenberg Lagrangian

  2. Equation-of-motion operators

  3. Matching, photon-photon scattering at low energies

  4. Power counting and loop corrections

  5. Standard-Model Effective Theory (extra slides)

Lecture 3: Renormalization (notes, video)

  1. Fermi theory for charged-current quark decay

  2. Renormalization and operator mixing, renormalization group (RG)

  3. Resummation by RG evolution: RG improved perturbation theory

Lecture 4: Modern Effective Field Theory (notes, video)

  1. Soft Effective Theory: soft photons in electron-electron scattering

  2. Expansion of loop integrals and the method of regions

Thomas Becher

ITP, University of Bern