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Effective Field Theories

Module PH2122

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2018

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2022/3SS 2020WS 2018/9SS 2018WS 2016/7SS 2011

Basic Information

PH2122 is a semester module in English or German language at Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
300 h 60 h 10 CP

Responsible coordinator of the module PH2122 in the version of SS 2018 was Antonio Vairo.

Content, Learning Outcome and Preconditions


The lecture course will provide an introduction to effective field theories (EFTs) and renormalization techniques with applications ranging from high energy to atomic physics. The following topics will be covered:

  • Principles of EFTs
    • Scales and systems in nature
    • What is an EFT and how to construct it
    • Example: the Euler-Heisenberg Lagrangian
    • Example: the Fermi theory of weak interactions at tree level
    • Example: the Rayleigh scattering
    • Relevant, irrelevant and marginal operators
    • Quantum loops of irrelevant operators
    • Mass-dependent vs mass-independent regularization schemes
    • Dimensional regularization
    • Quantum loops of marginal operators
    • Example: β function and running coupling constant in QED and QCD
    • Decoupling theorem
    • Example: the one and two loop matching of the QCD strong-coupling constant in MSbar
    • Renormalization group equations in QFTs and EFTs
    • Anomalous dimensions
    • Mixing
    • Example: ΔS = 2 transition amplitude in the Fermi theory of weak interactions
  • Heavy quark effective theory
    • Heavy-light meson spectrum
    • Heavy-quark spin-flavour symmetry
    • Static Lagrangian
    • Spectroscopy implications
    • Heavy meson decay constants
    • Transition form factors: Isgur-Wise functions
    • Example: B → D transitions and calculation of dΓ(B → D e ν)/dq²
    • Renormalization of composite operators
    • Example: heavy-light currents and heavy-heavy currents
    • Heavy meson decay constants at LL and NLO
    • The 1/m expansion of the HQET Lagrangian
    • Reparameterization invariance
    • Chromomagnetic coupling and hyperfine splitting at LL
    • Decoupling in the HQET
    • B → D e ν and Luke's theorem
  • Applications to atomic physics
    • Bound states in QED: physical picture, scales, degrees of freedom
    • NRQED: Lagrangian, power counting, matching
    • Four-fermion operators
    • Example: matching of dimension six four-fermion operators and the positronium decay width
    • pNRQED: Lagrangian, power counting, matching
    • Example: the hydrogen atom and the Lamb shift
    • Example: the Rayleigh scattering in pNRQED

Learning Outcome

The student will aquire the necessary knowledge to build effective field theories, compute Wilson coefficients, renormalize them, solve renormalization group equations and compute observables in principle at any order in the expansion parameter(s). In practice we will work out one loop calculations for non-relativistic effective field theories in QED and QCD.


Quantum Mechanics 1 + 2 and some basic knowledge of Quantum Field Theory and the Standard Model.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Effective Field Theories Vairo, A. Tue, 14:00–16:00, PH 3343
Thu, 10:00–12:00, PH 3343

Learning and Teaching Methods

Lectures will be given on a blackboard. Many physical examples will be presented and worked out in all details. Exercises are suggested and will be discussed as requested. Discussions and feedbacks during the lectures  are strongly encouraged.


accompanying website



  • Principles of EFTs
    • Books:A. Dobado, A. Gomez-Nicola, A.L. Maroto, J.R. Pelaez, Effective Lagrangians for the Standard Model, Springer Verlag 1997
      S. Weinberg, The Quantum Theory of Fields Vol. II, Cambridge University Press 1996, Chapter 19
    • Review papers and lecture notes:A. Pich, Effective field theory, Les Houches 1997, Probing the standard model of particle interactions, Pt. 2* 949-1049, e-Print: hep-ph/9806303
      A.V. Manohar, Effective field theories, Schladming 1996, Perturbative and nonperturbative aspects of quantum field theory* 311-362, e-Print: hep-ph/9606222
      D.B. Kaplan, Effective field theories, 7th Summer School in Nuclear Physics Symmetries, Seattle, e-Print: nucl-th/9506035
      H. Georgi, Effective field theory, Ann.Rev.Nucl.Part.Sci.43:209-252,1993
      B.R. Holstein, Effective effective interactions, Eur.Phys.J.A18:227-230,2003
    • A founding paper:S. Weinberg, Phenomenological Lagrangians, Physica A96:327,1979
    • EFTs courses:School on Flavor Physics, Centro de Ciencias de Benasque (2008)
      Effective field theory course (2013) at MIT by Iain Stewart (with emphasis on SCET)
  • Heavy quark effective theory
  • Books:A.V. Manohar, M.B. Wise, Heavy quark physics, Cambridge University Press 2000
    • Review papers and lecture notes: M. Neubert, Heavy-quark symmetry, Phys.Rept.245:259-396,1994
      B. Grinstein, An introduction to heavy mesons, 6th Mexican School of Particles and Fields, Villahermosa, e-Print: hep-ph/9508227
      T. Mannel, Heavy-quark effective field theory, Rept.Prog.Phys.60:1113-1172,1997
    • Related papers:G.P. Lepage, L. Magnea, C. Nakhleh, U. Magnea, K. Hornbostel, Improved nonrelativistic QCD for heavy quark physics, Phys.Rev.D46:4052-4067,1992, e-Print: hep-lat/9205007
      A.V. Manohar, The HQET/NRQCD Lagrangian to order α/m^3, Phys.Rev.D56:230-237,1997, e-Print: hep-ph/9701294
  • Applications to atomic physics
    • Related papers:W.E. Caswell, G.P. Lepage, Effective Lagrangians for bound state problems in QED, QCD, and other field theories, Phys.Lett.B167:437,1986
      A. Pineda, J. Soto, The Lamb shift in dimensional regularization, Phys.Lett.B420:391-396,1998, e-Print: hep-ph/9711292
      A. Pineda, J. Soto, Potential NRQED: the positronium case, Phys.Rev.D59:016005,1999, e-Print: hep-ph/9805424
      B.R. Holstein, Blue skies and effective interactions, American Journal of Physics 67:422,1999

Module Exam

Description of exams and course work

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

  • Typical questions will include: how to construct an EFT, how to match it, how to write an RG equation,
  • how to write an RG equation. Specific physical examples presented during the lecture (HQET,NRQED,pNRQED, etc.) may be also discussed.

Exam Repetition

The exam may be repeated at the end of the semester.

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