Effective Field Theories

This lecture provides an introduction to the framework of low energy effective field theories. After developing the basic concepts, the method is used to analyze the electromagnetic, weak and strong interactions at low energies. The course is intended for master students, who have taken a first course in quantum field theory.

There is an ILIAS page for discussions and further information.

This lecture was first given in the spring semester 2010, and was offered again in 2015 with a somewhat different selection of topics. The lecture notes are linked below.

Update (May 2021): The handwritten lectures notes linked below were typeset in LaTeX by Jonas Haldemann in 2015. They have been revised and corrected by Martin Hoferichter for a course in 2021. Here is the resulting PDF script (70 pages, 1MB).

  1. Introduction (and some introductionary slides)
  2. The Wilsonian effective action
    1. Integrating out high-energy modes
    2. Classification of operators
    3. Renormalization group
  3. Continuum effective theory
    1. Tree-level matching calculations
    2. Field redefinitions
    3. Matching at higher orders
    4. Power counting
    5. Renormalization group improved perturbation theory
  4. The Standard Model at low energies
    1. Euler Heisenberg Theory
    2. Decoupling of heavy flavors
      1. Decoupling in QED (Figures: anomalous magnetic moment)
      2. Heavy flavors in QCD (Figures: running coupling)
    3. Effective weak Hamiltonian (Fermi Theory)
    4. The Standard Model as an EFT (slides with operators)
    5. Chiral Perturbation Theory
      1. Chiral symmetry
      2. Transformation properties of Goldstone bosons
      3. Effective Lagrangian
      4. Applications (figures)
  5. Non-relativistic theories
    1. Heavy-Quark Effective Theory (HQET)
      1. Connection to quantum mechanics
      2. Applications of HQET (figures)
    2. Non-relativistic QCD and QED
  6. Energetic particles and jet physics
    1. Asymptotic expansions and the method of regions
    2. Soft-Collinear Effective Theory

Appendices

  1. Loop integrals in dimensional regularization
  2. Feynman rules for derivative couplings
  3. QCD Lagrangian and Feynman rules
  4. Goldstone's theorem

Exercises
  1. Exercise 1
  2. Exercise 2
  3. Exercise 3
  4. Exercise 4
  5. Exercise 5
  6. Exercise 6
Solutions to some of the exercises by Monika Hager: Exercise 4, Exercise 5, Exercise 6.

Thomas Becher

ITP, University of Bern